It will be very revealing to see how many teams actually pull this off. The general feeling is most teams, like America at large, have a 70-75% "willingness" rate. I would think that with what is at stake here, teams will be able to convert their stragglers. But this situation is exactly why it's going to be harder to achieve true herd immunity to the point of packed arenas/concerts etc. I just don't see any evidence that "most people" are going to get vaccinated. Most in that it will be a majority, yes but not the number we really want (which is indeed above 80%).
The vaccine passport issue is actually cut-and-dried if you take away the culture war obfuscation (impossible I know). Unfortunately the anti-vax crowd has already had success keeping government entities, including schools, from requiring them (you may not realize that as much on the East Coast - out west, it comes from both the far right and the "natural" left, and the Portland-adjacent Southern Washington area no longer has measles under control).
But to suggest that private entities can't do that is just more hypocrisy from the freedom crowd. I suppose the grey area is that while MLB and the Phillies and concerts are private, often the land on which the venues sit, and/or the venues themselves, are not. Ditto the air travel system in general.
There will be lawsuits. It also remains to be seen how the variants and need for booster shots play out.