When the government pays for part of college tuition it rewards people for increasing their own human capital. The smarter a person the better work they can achieve. College isn't cheap and increasing the costs is a bad idea. "astronomical student-debt levels, which long since crested above $1 trillion."(thenation.com)
Free college also means more taxpayer dollars, as the taxpayers will have to pay for the entirety of the college. College is more expensive in the long run for everyone. "It's easy enough to see that as subsidies have increased then the price of college tuition has increased."(forbes)
I believe that college should stay subsidized because some people seriously can't afford college if the price was increased. The current subsidization is working well, even if it costs a little more than what most taxpayers would like.