I mean, there are millions of athletes out there who would gladly play in the NFL for far less money than the Union players wanted, so why didn't they just run a scab league?
Maybe its because the fans want to see the best product available.
If the SEC suddenly stopped giving scholarships to athletes, the money would dry up real fast. Sure, there are fans who would still go to games just because MSU is their school, but you wouldn't see 100,000 people in the stands at Bryant-Denny, CBS would no longer pay the big TV money, and you wouldn't pay a guy like Nick Saban $5 million per year to coach your non-scholarship players.
College football and basketball are HUGE businesses. They generate TV and ticket revenue, and account for the vast majority of donations to Booster Clubs. Having good teams also increases merchandise sale and academic donations, so the Universities directly benefit from on-field success as well.
Now, some of that money would be generated no matter who is wearing the uniform....it's just a fact of organized sports that you have a certain level of fan interest even if the product on the field sucks (Hell, the Saints ran their entire organization on that principle before Benson came along). But that guaranteed revenue only goes so far.
Successful performance jacks up the revenue in many ways. Yes, most of that money is re-invested into the non-revenue sports, but the players deserve a little of that jack, too, particularly the money made off of their own image. The first place to turn for that money is the coaches' salaries. Saban already said he would be willing to share some of his salary with his players....tell him to put up or shut up.
The problem is, as much as the players deserve the money, there is no decent way to give them the money without upsetting competitive balance. Even this modest stipend threatens to screw things up since a) not all schools can afford the stipend; and b) it just opens up more ways to hide illegal payments to players.