Let's be clear what you're suggesting here: universities that are doing well on their current tuition, and would still be making the same money in the case of government subsidies, would spike their tuition costs by $10,000+ / year just for extra profit "because they can", despite not needing to, and screwing over everyone in the process.
I'm not saying it won't happen, I'm just saying that paints a dark picture of humanity and its almost certainly doomed future if it does and isn't corralled.
(BTW, I wonder how the European countries that offer socialized university have countered that effect?)
That's literally why college is so damned expensive to begin with.
Of course they're going to raise prices because they can - that's literally how every business works.
The majority of politicians have connections with people who are highly business-informed who know how to parlay corporate profits into well meaning sounding legislation. That creates a win-win in public perception while simultaneously fleecing the public coffers.
I do not expect this trend to end.
Then perhaps you've hit upon the root of the problem: education shouldn't be run like a business.
Government involvement is part of the reason we're here. A college charging more money isn't 'dark'--they too have bills. Attending a college to major in something is an investment which should include a cost/benefit analysis.
Which they are currently able to pay. Governments subsidizing student loans doesn't increase the bills for the college.
Of course there should be a cost/benefit analysis. There should be a cost/benefit analysis for any decision. That doesn't mean it's right for the costs to be artificially inflated beyond what's necessary.
Much like a house, nobody really cares about the sticker price, at least as long as it doesn't lose a ton of money. They care about the monthly payment. And even if interest is 0%, you still have a monthly payment for the principal.
(in some ways, college is even worse than houses since at the time of the loan you really don't know what the monthly payment will be at all... it's just magic money. And in fact your payments can heavily vary based on your income (although you'll still accrue interest) and how long you want to pay it back over.)
Setting 0% interest without some fundamental reform of college costs just kicks the can down the road and allows colleges to balloon costs even further since welp, payments are lower now, so you can afford more, right? You always still have to pay that principal though, so it really is just can kicking - at some point costs will balloon enough that 0% interest still has unaffordable payments merely on the principal itself.
I disagree that it will be "instantly" raising tuition but in the long term yeah, eventually any money that you throw at students (grants, loans, 0% loans, loan forgiveness, etc) is going to be swallowed up by colleges as long as they can get away with it.
Fundamentally, cost controls at "state universities" (and similar public institutions) have to be instituted at some point. I don't have a magic wand for how to make schools run more efficiently - administrators seem to be a problem, excessive construction and remodeling seems to be a problem, sports programs seem to be a problem (almost all are run at a huge loss except for colleges that can manage top-10 status in whatever sport). But as a more general statement, colleges are responding to what they think the market wants, and responding to the perception that if they don't, their competition will and they'll lose students. So this is a situation that's pretty ripe for some kind of regulation at public institutions - it's a clear "market failure" where the market is not giving the desired outcome. The public institutions will, in turn, keep a ceiling on the private institutions, and provide a reasonable alternative.
Unfortunately that will require congressional action - much like the "retroactive 0% would be better than $X loan forgiveness for current students!" idea, it simply will never actually get passed so it's not really an option within the current Overton window. And even if democrats proposed it, republicans would simply say no, they are in opposition to ANYTHING that democrats could count as a win or achievement regardless of whether it's right/wrong or good policy (see: burn pit disability).