Why are you thinking about this in zero-sum free-market terms? We live in a society. There are benefits to getting a college education beyond just developing job skills. That mindset is part of the reason why we're in this mess. But let me try to steer clear of the "in defence of humanities" argument and address this on your terms.
I've worked for colleges where over 50% of incoming students needed remedial Math and English classes before they could even start the 101's. They were functionally illiterate, even though they all graduated from HS, most with great grades. Subsidizing college is not about solving problems at the top, it's about addressing the systemic inequality that is a drag on the economy. If you need to take 2 or even 3 semesters of remedial coursework, that's eating into your financial aid money. I can't count how many times I've seen students drop out in their last year because they had a balance of under $500 and couldn't afford to graduate. This at a large public college in NYC that serves some very poor people.
I question your "overqualified workforce" argument. My experience as a STEM student in college and later as a college administrator has time and again indicated that hordes of HS graduates are completely unprepared for college level coursework. A lot of private philanthropy money and public grant money gets dumped into STEM initiatives at the college level. Even shitty colleges can get access to this funding, STEM grant industry is an industry that buys its own bullshit. Sure, MIT and Stanford and a bunch of great schools are making good use of this money. At many other lower-tier colleges, this money just gets wasted. The biggest problem is often that the grant money hasn't been spent, and suddenly there's a scramble to buy whatever bullshit equipment in the last minute just to have some bullshit to report to the grantor.
Again, you can't approach college education like it's just a business of making qualified workers for other businesses. The students come in unprepared. They can't read. They lack basic math skills. A semester or 2 of remedial courses taught by underqualified adjuncts will not solve that. And then you throw them into engineering and science classes and watch them drown. So what do these colleges do? Well, they do what any business would do. They can't change the quality of the raw materials (students) and they depend heavily on tuition money, as state and federal funding has been steadily decreasing over the past few decades. So they can't just raise the standards either, because then there would be no students, no tuition and no financial aid money and they would be forced to do all sorts of unpleasant downsizing, many would shut down. Meanwhile, the student debt has skyrocketed, beyond credit card debt, etc. You have basically a quarter of the population about to retire.
What we need is a profound reform of the K-12 public school system and privatizing it via vouchers ain't it - it doesn't work for higher ed, there's no reason to think it can work on the K-12 level. Education should never have been allowed to become a business. All of this hyperbolic excellence this and readiness that oratory is corporate speak that's invaded the educational system with private money and boils down to one thing - buying their own bullshit hush hush circlejerk where everyone gets paid. You can't default on a student loan. The gov't won't let it, they're guaranteeing these loans. This is a bubble. What happens when this gigantic swarm of old people retires? How is the working population supposed to pay for the baby boomers social security payments and medicare when they're drowning in debt? There is a conceivable future situation where dropping out of the workforce is the logical choice.
And the solution is not to shut down all the colleges that aren't hitting post graduation employment benchmarks. A bunch should be shut down, the for-profit ones for sure; and many shitty little non-profit ones that get by on one or two fancy sounding Mechatronics or whatever the fuck majors that let them both attract a bunch of students who buy into this predatory shit and get gov't and (these types of colleges to a lesser degree) private grants. This is free money and the post graduation employment numbers can be (and are) fudged in countless ways.
Ok that right there was an angry digression, let me try to get back to my point. You can't just shut them all down and say there, cost-cutting like a pro manager, where's my fucking bonus? These kids still can't fucking read! What job are they going to do? A US college education now serves the function of getting you to a point where you can function and adapt to circumstances, exactly what a HS degree used to do. In many countries the HS degree still does that, but we've been running this shit like a business and not like a public service. Again, what happens when all these people retire, all these kids are shit out of luck, uneducated, underemployed, in debt and angry? It's already happening. This is a perfect situation for a demagogue like Trump to show up and offer lazy solutions like "winning", building big walls. Back to my first point about us being a society first - this is how you erode it. And Sanders' suggestion, which is not all that original nor incredibly wide in scope, is to start addressing it by offering poor and middle class kids an opportunity to get some basic skills without ruining their financial future. Starting at the college level makes sense to me, until you can address the bigger issue - the atrocious state of K-12 public and private schools.
And let me just end with a decrescendo here - there are hundreds of thousands of incredibly bright kids who got to go to decent-to-great schools and moved on to decent-to-great colleges and are now working some type of job (some are changing the world with the next fucking app that lets me summon one of these unlucky underemployed fucks to wipe my ass with a press of a button) and paying off their college loans. These kids are the smaller chunk of your problem here, they won't do as good as their parents but they'll live. The issue are the hordes of kids who were never given a chance, and that's the kind of shit that gets to bite you in the ass years down the line.