If the school has overbooked students:parking then its a scam to offer parking permits to students who probabilistically will never find a parking spot without resorting to the extremes (time or distance). There's no reason to offer a permit (or charge for it).
I don't think its because of cars. There wont ever be a high quality uni in walking distance for 20,000+ people simultaneously.
there's also cycling and public transport. a single parking spot can fit up to 12 bikes and - in a perfect world - there'd be park & ride facilities on the city outskirts with tram connections to the uni. thus you wouldn't have to drive your car through rush hour city traffic.
I don't think its because of cars. There wont ever be a high quality uni in walking distance for 20,000+ people simultaneously.