When the government subsidizes something, its cost rise, because the market will bear more money for it.
That explains why food costs so much, from all the government subsidies to farmers. Same thing for gasoline. The billions of dollars in subsidies oil companies receive each year is driving up the cost for consumers. And let us not forget sugar. Sugar would be far cheaper, and could be used instead of subsidized corn syrup, were it not for the sugar subsidies.
Excellent sarcasm, smooth wombat; I laughed. I presume you know how these subsidies are different, so I'll write out for others' sake: Suppose people want diamond tennis bracelets from Tiffany's, but they have a hard time buying them because the bracelets cost so much. Now a rich person for some reason wants to help more people get bracelets from Tiffany's and offers to give everyone half the cost of the bracelet, making them easier to buy. This works to expand access, only until Tiffany's learns about the deal. Once Tiffany's knows this is the deal, they can double their price and still sell as many bracelets as they used to, but make a lot of extra money from fleecing the rich guy. If they raise it less than double, customers are still getting a slightly better deal than before rich guy showed up, so they're happy to buy, and again, Tiffany's is making a bunch of extra money.
Now swap Tiffany's/colleges, bracelets/degrees, rich guy/federal government, half the cost/some need-based FAFSA calculated amount, and you're pretty close to reality. Colleges keep their status character by continuing to be selective in their admissions, and if everyone shows up with a government-padded wallet, that's less financial aid the college needs to give to attract customers. They can put more money into posh facilities and paying football coaches far more than professors, because everyone gets federal financial aid which they immediately cosign over to the college. Because people don't truly care about sticker price for college any more than they do for surgery when they have good insurance: they care about what they pay out of pocket, and to a lesser extent, how much they can tell people they saved off the sticker price thanks to loans/grants/insurance.
There are at least two other big wrinkles in the government education subsidy story, and they're probably what drive anyone to care about them. First, we may collectively believe that an educated society is a valuable thing, and that getting more college graduates is a way to achieve that, and therefore we like these subsidies. Second, we may acknowledge that the money doesn't come from thin air but comes from government's power to tax us, and may have feelings about what else the government could do with the taxes it collects, what else we could spend our money on if not taxes, who should pay how much in taxes and why, or about the efficiency of central taxation and distribution versus individual and local decision-making. But those are worthy of their own threads.