First off let's get something totally clear. Essentially no one says that the American workforce is over-qualified or over-educated. There is little to no debate as to whether higher education is valuable, but the questions are always what kinds of education are best and if it's worth public investment.
Children have been told since their infancy that college is some innate good; with such repetition and consensus, it's not to hard to understand why a lot of students are obsessively compelled to shoot for a Bachelor's degree even when they have no idea of what to study nor any desire to find out. Too often students just pick their favorite subject in high-school as their major without thinking too hardly on what they can do with it.
The Sheepskin Effect
Any high-school student knows that salaries for college graduates are higher than non-graduates; it's been pounded into their heads by their teachers and principals looking to maximize college enrollment from their institution. A person who is higher in the degree hierarchy, with all things constant (including actual productivity) will be paid more than an otherwise equally qualified worker who didn't graduate. This is called the Sheepskin Effect, deriving its name from the fact that degrees were once often made of sheepskin.
With the Sheepskin Effect alone, college graduates aren't necessarily paid more because they're universally better equipped and more efficient employees that their pre-bachelor counterparts, but when employers choose to hire a worker and decide how much to pay him, they have to rely on generalizations to estimate how good f an investment a worker is. Two workers may be nearly equivalent, but in the case of a hiring decision, the one that has better certification and skills, a degree, the ability to speak other languages, work experience etc. will have a better chance of being hired and then paid more.
The Sheepskin effect thus designates that having a degree, even a functionally worthless one, at least tells employers with imperfect information that you're at least capable of pushing yourself through a curriculum. It's just an advantage in signaling for the job applicant.
Efficiency and Specialization
There are some sad people who don't earn degrees for any reason other than to reinforce their résumés and take advantage of the Sheepskin Effect, but the main rationale for going into higher education is to actually make one's self a more efficient and attractive employee or to give one the skills to be self-employed. Taking courses aren't hoops you have to jump through to get a prize; they're opportunities to expose you to new skills and knowledge.
There are plenty of careers that necessitate depthy knowledge of a subject to even be able to compete. For students studying biology, chemistry and other sciences, a lot of the classroom content and activities are not accessible to people outside of the lab or the classroom. It may be true that a student can read everything required for a sociology degree on Wikipedia, but for the hard (read: useful) sciences, hands-on participation in academia, even at a superficial level is a necessary precondition for a productive post-graduate career.
So what are the undesirables of a degree?
Ask any current student or recent graduate what the main difficulty of higher education is and they're likely to say it's the high price and the debt many students accumulate. I'd at least say that debt is more of a psychological factor, most federal loans are either partially or fully subsidized and it's pretty hard to find more friendly interest rates anywhere. A student may be paying debt off for many years, but I don't know of anyone who has been reduced to poverty because of said loans.
For many students, student loans constitute their first fleeting contacts with financial adulthood. In a sense they realize that a lot of the services they have for so long received are not in fact free, and they do, in a very tangible sense, finally owe society something back. Of course these realizations are experienced by some students more readily than by others; the early twenties is a time where entitlement must painfully metamorph in responsibility, and many students have trouble with this.
Debt can be overcome, even by a student whose education didn't afford him more efficiency. What is truly dangerous about a superficial education is the fact that it can make workers, in Joseph Schumpeter's words "psychically unemployable" in lines of work they deem beneath them. A student who has just spent nearly $200,000 in a first tier university, or even several thousands in a state college for an English degree is unlikely to take any kind of manual labor, or really any job that gains them less 60-70 thousand a year. For English majors, that will basically never happen.
Often times undergraduate students choose degrees and specialties that coincide with what they want to do and expect there to be gainful employment directly after running a typical undergraduate curriculum. That's not how it works. Nowadays the "American Dream" has been deformed into the idea that every child should go to school in whatever they want and then be awarded with a job that precisely coincides with what they like to do in their spare time. In reality, not everyone can be an astronaut; a lot of growing up is bending one's self to fit where needed.
Public Waste
Now essentially all institutions, private and public receive direct or indirect state aid, but states will generally pick up the tab for a lot of public universities. At the public university where I got my undergraduate education, tuition and fees per semester for a full-time student were usually about $15,000. Most students would never even see a bill remotely that high because the state picks up $10,000 of that instantly in the form of instate tuition waivers. That way, instate students like myself would only have to pay the remaining $5,000 (state-funded merit scholarships would generally slice this down to 1-2 thousand in out-of-pocket funds but this wouldn't apply to all states or to students below a certain GPA).
Regardless, state governments that sponsor instate tuition waivers would pay those $10,000 dollars for every student in every state university every semester. It's still quite a good deal to pay about $80,000 to have a fully-trained bachelor's-holding graduate, but for every student who drops out without a degree, having only finished several core curriculum classes, the government ends up pittering away large sums just to have recent high-school graduates take English composition and history classes again at a university.
The perverse incentive is that individual state universities don't necessarily have any reason to weed out undedicated students in their application process. In my state, as in basically all others, nearly all state universities have undergraduate acceptance rates far better than a coin-flip. Universities don't bear the cost of instate tuition waivers, but they can generate more income by signing on unqualified students to pay tuition and fees for several semesters before they realize that college is not for them. A lot of state universities end up with an "underclass" of students who don't have any ambitions of finishing degrees; the universities themselves don't so much mind keeping them around to pay, but the state hemorrhages money on their classes that don't necessarily make them better for employers or more productive in any way.
BA in Sociology ≠ BS in Engineering
Another rumor that should be eradicated right away is the idea that all Bachelor's degrees are pretty much the same in usage. I remember being told this my high-school teachers quite often, and that's because for their purposes, it is true. To teach in a public school, all you really need is any higher degree (preferably of the topic you wish to teach in) and good knowledge of the curriculum, often enforced by standardized tests. My younger brother went to the same high-school as I did, and by that time a lot of the same teachers still worked there, but simply taught different subjects. That's normal in basic schooling.
In every other sector of life specialization is essential. If you want to study biology, you don't just need a degree, you nearly always need good lab-time in your undergraduate career and collaboration with the professors at your institution. Your undergraduate work is not the classes you have to take, it's how you can put your foot in the door of academia and contribute valuably to the work of your professors when possible.
This said, majoring in sociology and sending a graduate school an essay of you deconstructing gender roles will not get you into the grad program of your dreams. The Sheepskin Effect only goes so far, and it radically diminishes when you become involved with people who actually know what they're talking about.
Ultimately degrees are not supposed to demonstrate that you can plow your way through coursework; they're meant to show that you have a good working knowledge of a specific topic of study. If you major in economics, that should indicate to potential employers and graduate schools that your have a good familiarity with econometrics and the calculus that supports it, economic theory, international trade, and public policy. If you major in African American studies, what does this indicate to employers? Maybe a level of cultural understanding, maybe a good knowledge of American cultural history, but not nearly enough to land a fulfilling job. I would be willing to be that black advocacy groups would perhaps be even more willing to hire an economics student who knows about urban economics and public policy than a garden variety African American studies major.
Ponzi Schemes
I was at a meeting of my university's Latin Club recently joking with the other Latinites about how pathetically worthless it is to actually study the language. All of us had come a long way to know Latin's sublime grammatical subtleties so it's always a little sour to joke about all the time we've "wasted." One of them noted that all of Latin pedagogy is a huge "Ponzi Scheme:" Latin teachers and researchers only exist to attract more Latin pupils to study Latin and continue the cycle. That's the litmus test for near worthlessness in a degree: if the only activity that fully utilizes the skills you've gained is teaching the subject to another generation of students, it may be time to switch emphases.
I don't regret studying Latin or Greek, not even an iota, in fact, my only regret is not having begun studying them earlier. But there is simply no plausible circumstances under which I would have actually chosen to pursue them as a career. There may be some people who would like nothing more than to study the classics, but they'll have to compete with all the others like them to do so, it's too risky for me. There's nothing wrong with studying what you "love," but in college you should always look for what the best deal is economically for you. It's not greedy if you can set yourself up nicely you can better pursue your side interests anyway. People who major in Classics, English or <anything> Studies ultimately don't earn so little because society is cruel and inartistic; they earn little because their studies don't perform tasks that please others to the point of wanting to give them money to do said tasks. So if anything I'd say it's selfish to "follow your dreams" and expect to be remunerated for it, while to major in engineering, science or business is very much to bend oneself to where society best needs him.
Tweaks to Public Funding
I have to say I think that however unpopular such reforms would be, there are really obvious ways to improve public education without actually spending more. The key is really just to change public tuition waivers and scholarship based on the area of study of the student. My state has had to perform tiring gymnastics to reform their merit-based scholarship in recent years but to me the solution is obvious: don't subsidize a student studying art and another studying neuroscience equally. Even in an artists' most wild and narcissistic dreams, he will never contribute to society in a way that will compare to a rudimentary brain surgeon or neurologist; the state frankly shouldn't afford all areas of study equally.
Want to be a scientist or engineer? For all the difficultly in such a long-term investment you really should get a nearly full ride through your undergraduate career; the state will benefit from its investment in you. Are you passionate about art? That's fine, and maybe you should pursue your dreams, but you should know that even if your art inspires joy and even if it brings some drips of commerce to your community, you will not heal the sick or build housing, offices and restaurants.
So I would suggest state funded education for about half the credit hours required for a degree, but once a student must make a choice as to their area of study, the subsidy should correspond roughly to the social returns of the degree in question. This way there will be an incentive to leave bloated programs in literature and cultural studies and join the sciences and analytical crafts. A lot of people remain art majors, that's fine, but the state can save some money in not subsidizing their relatively inert education. If by an incredible education-elasticity all student major in sciences, then at least the state's investment is going further.