The thing is, part of that brand is based on the fact that people think they're watching college students play sports. They're not.
Serious fans, media, players, coaches, etc all know schools give players extra benefits, money, etc. We're not innocent, just like any major program is highly unlikely to be innocent. If it's not money to the kids, it's money to the parents to get them to go to a certain school. If not that, it's a free car to drive from a booster who runs a car dealership, or a job paying $10,000 an hour to mow the lawn in the summer, or a no/super low interest loan for an exorbitant amount of money based on the fact that the player is likely to end up in the NBA.
Casual fans tune in each March and think they're watching amateur basketball with the occasional scandal. It's really just the occasional scandal that sees the light of day. Until someone with the platform to do so really speaks up, we won't see change... But by then it may be too late, unfortunately. Meanwhile, the programs that aren't as good at doing the cheating that everybody knows is going on get caught and those kids get punished. They're just cogs in the big system, in which someone needs to be punished every now and then in order to attempt to preserve that pristine image of "student athletes."
I'm not saying paying players is the answer, because then there would be cheating to provide extra benefits beyond those allowed, but what we have now isn't the answer either. If they maintain the new APR rules, schools will either get better at cheating or the NCAA will dissolve and the super conferences will form a new association and have their own tournament.
As a first step, I'd suggest making sure that anybody that leaves a school early doesn't cost the school APR points. As a second step, I'd suggest that trust funds be set up for players. Each player would get a share of the revenue from video games, broadcast rights, etc, but it wouldn't pay out until they hit a certain age (30 maybe?). Players who had a jersey sold by the school would get an extra amount, since schools can sell three numbered jerseys (no names) and they have to pick each year. Funny how the numbers just so happen to be the ones of the most popular and best players on the team, but they still aren't marketing that player. Give me a break. Players should also retain the right to their image after X years go by. For example, NCAA basketball video games have historic moments and the players just so happen to wear the same number and look the same as the real life players, but they have no claim to compensation. I think once they're no longer playing in the NCAA, they should have the right to market their past image. If a video game company wants to, for example, have you play as Gerry in the 2006 Big East Tourney and hit the same shots, he should now profit off of that.
At least this would set up SOME compensation for players, even if it's after the fact. It would keep it "amateur" at the time, and perhaps any player caught taking money would lose his future rights, to try to actually clean it up a bit. It would also give players a little more reason to stay around for an extra year if their decision were close.