I don’t have to narrowly define a market nor do I have to establish market power in the context of litigation alleging violations of the Sherman Act. The NCAA themselves have twice tried to argue what you’re suggesting and both times were soundly defeated in court. So there is no need to even ask the question if the NCAA has market power in the market for selling one’s image (see excerpt below from appeal of Law v. NCAA).
By outright banning athletes from even pursuing endorsements, it is a naked restraint on output. Again, were you qualified to discuss this you’d understand that.
The NCAA misapprehends the purpose in antitrust law of market definition, which is not an end unto itself but rather exists to illuminate a practice's effect on competition. In Board of Regents, the Court rejected a nearly identical argument from the NCAA that a plan to sell television rights could not be condemned under the antitrust laws absent proof that the NCAA had power in the market for television programming. See 468 U.S. at 109, 104 S.Ct. at 2964. "As a matter of law, the absence of proof of market power does not justify a naked restriction on price or output. To the contrary, when there is an agreement not to compete in terms of price or output, 'no elaborate industry analysis is required to demonstrate the anticompetitive character of such an agreement.' " Id. (quoting National Soc'y of Prof'l Engineers, 435 U.S. at 692, 98 S.Ct. at 1365). No "proof of market power" is required where the very purpose and effect of a horizontal agreement is to fix prices so as to make them unresponsive to a competitive marketplace. See id. at 110, 104 S.Ct. at 2965. Thus, where a practice has obvious anticompetitive effects--as does price-fixing--there is no need to prove that the defendant possesses market power. Rather, the court is justified in proceeding directly to the question of whether the procompetitive justifications advanced for the restraint outweigh the anticompetitive effects under a "quick look" rule of reason. See Chicago Prof'l Sports, 961 F.2d at 674.