A good thought, but I'm not certain it works that way in this case. The laws of supply and demand may take over, here.
I have the (often unfortunate) distinction of being a member of the formerly-3 (now 2) unions for professional actors - SAG-AFTRA and Equity. Their founding is an interesting one, and could provide an interesting allegory to the upcoming shifts in college athletics.
In the 1920s through the 1950s, actors were employees of specific studios.They were under contract with a specific studio, with a deal for X pictures. What this did was allowed studios to be in control of an actor's career, with undue influence over it. The studios controlled an actor's schedule, which films they worked on, and their overall public image. If an actor upset the wrong studio boss, or if someone in power decided they didn't like the actor, the studio could simply sit on the contract forever and effectively "blacklist" the actor (
which happened to Bette Davis and Olivia de Havilland, among others). There was no ability to "transfer."
Additionally, studios owned the production facilities, the theaters where movies were distributed, and in some cases even the outside companies that processed film and generated special effects. They would often work with other studios to determine which independent theaters would be allowed to show certain films. They owned the distribution and the means of production, all of which prevented actors and independent producers from competing on the open market.
In 1948, a Supreme Court ruling deemed Paramount Studios a monopoly, and
effectively dismantled the studio system. And that's when things really started to change in the actors' world. The actors were now independent contractors, and could shop themselves around to other studios. Actors continued to collectively bargain - but now over more issues. Essentially, the producers and studios organization would meet with SAG/AFTRA and negotiate changes to the broad union contract, which set base levels of salaries, conditions, etc - all of which were effectively minimums. Actors could always negotiate more than the floor of the contract (and they still do, of course). This was all while actors were independent contractors, not employees.
The producers and studios negotiated
not because rank and file actors had leverage, but because the public wanted to see the stars, and the stars agreed to stop work until protections were afforded to actors of all income levels and public stature.
So while universities may not be bound to negotiate with the formerly-"student athletes," eventually there will be enough star power involved that the university ADs will have to take notice and negotiate.
Again, same as it ever was: billable hours will be what wins. And it will be interesting to see what the student athletes do when confronted with paying out union dues, paying for attorneys, dealing with union bureaucracy, having to focus less on the "me" and more on the "us," etc. But I'm pretty sure supply and demand will work in the athletes' favor here as far as getting universities to the table. If not Dartmouth, the precedent has now been set.
Given the whole sticky situation with schools supposedly being about education & all, I would expect to see athletes not go the route of the "W-2 employee" (as the NFL does), but adopt an IC model similar to what actors and directors in the entertainment industry do. This will allow schools to say "they are students, but we're paying them for another thing they contribute to the school." But that remains to be seen - as we know, there are a lot of litmus tests set up around what constitutes an IC versus an employee.
Anyway, thought I'd bring that up, as it continually jumps into my mind as this situation continues to develop. I would be shocked if the scenario of actors' business dealings doesn't continue to be a good analogy for the players' situation.