If you're driving around in a private vehicle as a college student you're probably already pretty privileged.

There's no way in a million years I could have afforded my own car as a student.

I saved money by living off-campus and driving to school using the cheap car that I also needed to get to work. There are a lot of places in the US like that, where you can't afford not to have a car.

> If that would seriously be the issue with free parking, then build parking garages.

This sidesteps the underlying decision of who pays for those garages. Either you charge for parking and the people who use it pay, or you don't and every student (even the ones who take the bus or carpool) pay.