Here are some counter arguments.
Roster limits would still be a factor. Kentucky can't literally get everybody. Part of the calculus a player makes will be weighing opportunity on a roster. Is it better for them to be the 10th man at Duke, or the top guy at Iowa State? That isn't much different from how players have to think of it now. In fact, bring in financials, and we might even see talent smooth out some.
Another factor will be geographic opportunity. It's very possible it becomes very valuable for athletes to dominate the market where their school is located. This likely means some previously overlooked destinations become very hot and desirable.
It's also possible that more money flows in. We have bag men because that's how a "donor" can drive the most direct impact to their program. Legitimate donors have to spend an awful lot of money to provide a ridiculous indirect benefit (locker room bling, for example). More people may step forward if they feel they can 1, directly benefit their favorite team more by coming to an arrangement with a player and oh by the way 2, actually derive some benefit from that relationship by having that player associated with their business.
We might also see some players clean up their act a little. It's one thing if you have the risk of losing a scholarship. It's another altogether if a public mishap during a night out on the town costs you 6 figures in endorsements.
Keep in mind too, most of the conversation so far has been about money going to a player as they choose a school. Let's not overlook though the value a player could realize while developing as an athlete. This is one of the biggest reasons why I think this needs to be done. We love in a world where under the right circumstances anybody can have their 15 minutes of Fame, and our current way of doing things prohibits student-athletes from benefitting from that. Think of the baseball player that makes news in town for throwing a perfect game, or women's softball players that demonstrate exceptional sportsmanship, or for Olympic sport athletes, imagine the benefit that an athlete at the top of their sport at a school could find when the US swim/wrestling/volleyball/gymnastics teams are popular during the Olympics. I think women's soccer players for example could be some of the biggest beneficiaries. One of the most compelling reasons to me to make a change is to benefit those athletes, and you can't predict all of that value or possibility until they're competing at that level.
Lastly, and I know you acknowledge this... big picture, this is a more important issue than how it affects any one University's fans and programs. I believe that rights to name and likeness are a necessity and inherent human rights in today's world.