You would quickly run out of places to take dates if you didn't have a car. Campus activities are great and all, but there is only so much variety that you can find. Also, your working opportunities would probably be limited to on-campus jobs. Hope you like grounds crew, dining services, or 4 AM custodial! That's not all of them, obviously, but those are by far the most common.
Otherwise, it's very realistic to live in Provo without a car. You can bike to the grocery store, walk to your classes, and catch a ride with friends or roommates for social outings.
If a car is too expensive, a scooter might be a good alternative.