Further, nothing is truly free. Were college free to all students, someone would still have to pay those bills. Public education is already the single largest expense of non-federal governments and a huge part of the federal expense. Increasing the scope of free public education would also significantly increase the costs involved - those costs must be borne by someone. So, you either pay for it now as tuition or you pay for it for the rest of your life in the form of taxes but either way, you'll pay for it.
And then there's the very valid point that all people aren't really "above average" in intellect and therefor all people aren't capable of attending and graduating from college. Our society would like to pretend that everyone is equal in motivation and intelligence but we know that's not really true. Don't we? What would be the result in terms of quality if we made college completely free to anyone?
Add to that problem - costs keep some people from attending. This is only bad in-as-much as it limits those individuals personally. But it's just that barrier that makes it possible for others to attend - college seats are not an unlimited resource of which we have plenty. There are only so many colleges with so many seats and more people would like to have those seats than can. If we removed the cost barrier then the competition for seats would be even greater and