The lower court in the Alston case laid out the antitrust issue, the Supreme Court agreed with its ruling, and everyone involved agreed that the conferences can ban NIL. They explicitly said it.
(What's below is much too long, so let me give what in Washington, D.C. they call an executive summary:
Conferences can do what they want but they can't collude. States can allow athletes to have NIL deals even if they're forbidden by the conference and the conferences have limited leverage over the states.
Now on to the details:
First, let me be persnickety and point out that the Alston case did not concern NIL, but rather educational benefits. But let's assume (as is probably but not certainly true) that the Alston case would be extended to prevent the NCAA from barring NIL.
The Supreme Court said in Alston that an individual conference can impose restrictions that go beyond what the NCAA can legally impose: but that multiconference agreements cannot. It is basic antitrust law that an agreement need not be in writing for it to be barred. Let me quote the U.S. Department of Justice:
"The agreement need not be embodied in express or formal contractual statements. It must merely constitute some form of mutual understanding that the parties will combine their efforts for a common, unlawful purpose."
https://www.justice.gov/archives/jm/antitrust-resource-manual-1-attorney-generals-policy-statement
Of course, it is not practical for a single conference to impose restrictions without others doing the same: kids who think they can get NIL contracts (that is, the best players) will simply go to schools in other conferences.
All those are the antitrust issues. As I've pointed out, there's also the problem of the state laws permitting NIL. This problem would continue to exist even if the antitrust issues magically went away; states can impose rules that go beyond what the federal courts require. In other words, the lower court and Supreme Court statements that federal antitrust law allows individual conferences to have restrictions that go beyond what the NCAA can have do not prevent the states from imposing their own regulations that go against those conference restrictions. Maybe the Big Ten, for instance, could intimidate one state into repealing its law permitting NIL by threatening to kick out the Big Ten member in that state; but it's harder to do that when, as at present, lots of states have NIL laws. As I pointed out, California is especially a problem. States permitted NIL because they became convinced that it is unfair for everyone to profit from a kid's athletic ability except the kid -- it's not going to be easy to get the states to reverse course.
So it's not surprising that the Big Ten, for instance, hasn't banned or sharply restricted NIL: it's just too risky. The Alston statement about what individual conferences can do is not helpful enough to the individual conferences.
Apologies if this was too long.
