I think the mistake is that people believe "someone" is going to offer them the money. That's not the case. Several sources will "offer them money," and it's the combined total from all of them, not a singular source.
As an example: At the University of Texas, there's a "group of businesses" that offered money to the offensive linemen. The total number, I don't know. But the idea behind this is that every one of them can use name and likeness in selling product and/or services. To top it off, they're not exclusive, there are more coming on board regularly, boosting the anti. The $50k was just the "base" of what these kids would get, there could easily be hundreds of thousands additionally, as long as it's not in direct competition to what the original deal makers line is.
You can look around and see these kids appearing on billboards, speaking in radio ads, in TV ads, pictures on menus, stating that's their favorite place for pizza, or other foods. Favorite store to buy pet food, groceries, and even places they get their hair cut. It's an endless number of revenue streams, and most of it consists of no more than a picture or two, which they add captions.
Good example, in Wisconsin. The TV ads for Hupy & Abraham. The shot a commercial with William Shatner, years ago. They paid him out front for doing it, and every time it airs, they pay him a residual. The same thing applies to these kids, in sports.
I have a cousin who makes millions of dollars every year by the money he gets for the repeated airings of movies he directed, scripts he wrote, films and TV productions, as well as the constant residuals he gets from three of the most successful TV shows on reruns throughout the world, that he's been part of since their concept.
You can't compartmentalize this as easy as people would like to believe it can be done. You gotta go completely outside the box to understand it. The money comes from everywhere. The thing that ties the kid to a particular school is those who buy their services/likeness, simply because they're willing to spend the money on it to promote their school. Also, remember, the vast majority of the money paid to them by these purchasers is tax deductible, as business expenses.