Replying separately to this one since it was added after I started my first reply.
I think the big difference is that the pro leagues have established a team/player relationship and top-level negotiated agreement that college sports lacks entirely.
Otherwise this example is somewhat similar-but-different to how MLB used their pre-1998 antitrust exemptions to avoid allowing free agency in the
Flood case before the Supreme Court. This was eventually curtailed by Congress, saying MLB players had the same rights and protections as other pro athletes, but by then the players had already gotten free agency through arbitration and then new labor contracts anyway.
Namely, the clause in question said the team reserved the rights to the player *even after contract expiration*.
And I haven't seen the wording of all scholarship agreements, but it looks like especially outside of P5 schools, it's common for them to be year-to-year agreements. So if the school can cut you loose after one year, why can't you cut the school loose? So I think that's a interesting example to look at for an example of how even in a more-negotiated-rules-setting, leagues have been ruled to only have so much power to require things in their contracts, and that reserve clause doesn't seem like it would've flied without an antitrust exemption. Ultimately the pro leagues ended up in a place of "you can have multi-year contracts, but you can't keep the rights to the players after that." And that would probably fly in college sports; maybe you'd even have a transfer rule so long as you're still paying the player, if the sides came to agreement on that.
But the NCAA is given a lot *less* leeway right now by the courts, I think in large part because their rules are being set by dictat instead of by negotiation at all.