Again, I am not writing this for you but for other people you may otherwise mislead. If you just look at the section of Kavanaugh's concurrence that you have quoted, in bold what he is saying is that the NCAA's prior business model violated antitrust law. That's the law they are not above. Again, that's his concurrence, which is Kavanaugh speaking for himself.
In the 9-0 SCOTUS opinion (that Kavanaugh joined, i.e. agreed with), as I have pointed out to you numerous times before in response to you quoting this section, the whole Court (i.e. every SCOTUS justice) signed off on the following:
"The “orderly way” to temper that Act's policy of competition is “by legislation and not by court decision.” Flood, 407 U.S. at 279, 92 S.Ct. 2099. The NCAA is free to argue that, “because of the special characteristics of [its] particular industry,” it should be exempt from the usual operation of the antitrust laws—but that appeal is “properly addressed to Congress.” National Soc. of Professional Engineers, 435 U.S. at 689, 98 S.Ct. 1355. Nor has Congress been insensitive to such requests. It has modified the antitrust laws for certain industries in the past, and it may do so again in the future. See, e.g., 7 U.S.C. §§ 291–292 (agricultural cooperatives); 15 U.S.C. §§ 1011–1013 (insurance); 15 U.S.C. §§ 1801–1804 (newspaper joint operating agreements). But until Congress says otherwise, the only law it has asked us to enforce is the Sherman Act, and that law is predicated on one assumption alone—“competition is the best method of allocating resources” in the Nation's economy. National Soc. of Professional Engineers, 435 U.S. at 695, 98 S.Ct. 1355."
Nat'l Collegiate Athletic Ass'n v. Alston, 594 U.S. 69, 96, 141 S. Ct. 2141, 2160, 210 L. Ed. 2d 314 (2021)
Congress could even re-install the old NCAA model if they wanted to, all they would have to do is fashion an anti-trust exemption to do so. Practically, no anti-trust exemption will pass Congress that does not include revenue sharing (nor should it), but anti-trust is Congress's law, they can change it largely as they see fit. SCOTUS itself said so, as can be seen above.