There are two reasons I disagree with you. Let me start with the one that has some chance of changing your mind.
I believe that spending on education is positive sum. That surely isn't always and everywhere true, but I believe that it's true at the margin, considering the conditions in the U.S. The book that originally convinced me of this was _Children as Pawns: The Politics of Educational Reform_, by Hacsi. It details, along with a lot of other evidence, a longitudinal randomized controlled trial (which is very rare in educational policy) which shows a positive benefit from additional education spending (admittedly, of a very specific type, and in one particular context). There's no way to provide a good summary of the evidence in the book, so let me just say that my opinion is that while the evidence is tenuous, the overall weight of the evidence indicates that the gains from education in tax revenue are greater than the costs. If you like, you can check out the book and decide for yourself. If you agree, then government funding of education seems like an obvious solution. And, of course, the overall gains to society are much greater than the increased tax revenue.
I don't mean to say that our educational system is particularly good. In fact, I think it's very inefficient in many ways. That doesn't preclude the previous conclusion, though.
The second reason is that, in the model above, college administrators capture much of the value added by subsidies. Some gain goes to "good" students, and "bad" students are severely penalized. I believe that's apparent from looking at the practical results, and you can see that in the model by adding student ability and graduation rate to the simple model above. You get an even more extreme result if you add types of degrees (hard vs. easy, with hard degrees resulting in more compensation. Typing out the entire "proof" would be tedious, but I can do it, if you disagree with the result of the model, given the premises. But, in the end, this is a philosophical difference. I don't think that we should be subsidizing college administrators (who are already much better off than average) and really good students (who, on average, will do fine in life anyway) at the expense of bad students (who, IMO, could use some help). I understand that a lot of folks would prefer that people are rewarded purely on talent. Having subsidized loans with a random probabilistic outcome magnifies that, so perhaps you think that solution is fair and just. If that's the case, and you're not convinced that spending on education is a net positive, then there's no hope my line of reasoning will convince you, and we'll have to agree to disagree.
I agree that incentive compatible solutions are important, but I don't think that creating a system that's efficient (in the sense that an econ 101 student would use the word) is the only thing we should consider.
P.S. Your original comment has been downvoted, but it wasn't by me. I disagree with your position, but I don't think you're arguing in bad faith or presenting even presenting a fallacious argument, which are the things I would downvote someone for.