Not all colleges charge a fee to use a credit card. My oldest child went to SUNY Binghamton and they did not charge a fee. My youngest is also going there, so I hope that is still the case. In the past I put my full bill on the card (approx $25K/yr). This is an amazing way to utilize a couple new credit cards with good intro offers.
Having said all that, I do pay off the card every month. I agree with the others here that I would never carry a balance. If I needed to, I would prefer a student loan at a better rate. I have the $25K/yr sitting in a 529 plan. When the large credit card bill comes in, I withdraw that amount from my 529 plan and pay the credit card bill.