There are legitimate points on both sides of this issue. Here are the best ones for the "don't pay them" position.
1. It wouldn't reflect economic reality. The vast majority of programs break even or lose money.
2. It can't be done legally without totally detonating the system. Title IX won't let you pay an outside linebacker but not a female swimmer.
3. Making the athletes essentially employees takes the college sports outside the realm of amateur athletics and creates just another professional league.
4. The day players are paid, the NCAA can kiss its tax exempt status goodbye. Congress isn't going to let a pseudo minor league go untaxed.
5. Entering into a scholarship is a voluntary transaction. If a player feels they are being exploited, they can always leave the university in search of someone who will give them what they want.
6. The legal ramifications of making athletes employees, i.e. worker's compensation, possible collective bargaining, et al, would bankrupt college sports in short order.