Earlier quoted context omitted.
Increase supply. Most schools use flat parking lots instead of multistory car parks which would be far more efficient. Alternatively, run public transportation that doesn't suck.
Building a bigger parking lot requires money... who should pay for that, all students or just students who drive? Why should non-driving students subsidize driving students? Also, the school is not in charge of public transportation.
Also, schools frequently are in charge of public transportation in the form of shuttles, buses, safe rides, etc.
Regarding subsidies, yes everyone should pay because it's a community and that's how communities maintain large collections of shared infrastructure equitably. Spreading the costs over a large group keeps them down for the individual users. Also, you can extend that logic infinitely. Why did I have to pay for football fields I never got to play on? Why did I have to pay for performing arts theaters I never used? Why did I have to pay for community facilities that weren't targeted towards my race or religion? Why did I have to pay for expensive research labs in departments other than mine? If you abandon the community model then everyone ends up getting slammed with highly variable usury taxes that they may not be able to pay.