I'd welcome you point me to where in the Constitution the antitrust right or prohibition exists. Believe it or not, price fixing has existed since the founding, and salary caps are part of every major sport. This isn't even remotely a constitutional issue.
Since 1890 there has been a pendulum swinging back and forth with the DOJ involvement in the market place ranging from 'big is bad' to the 'rule of reason'(or currently unreason) with anti trust enforcement.
The departing FTC chair Lina "Wrath of" Khan was an extreme example of big is bad. The pendulum has swung back to benign neglect.
I see the constitutional issue in the separation of powers and check and balances embedded in our constitutional order. That is the legislative branch can make legislation impacting merger/combination and price coordination activity and the judicial branch can rule on these pieces of legislation. Given the ambiguity of much "legislation" as we have seen recently, the executive branch can chose or not chose to enforce.
In sport, we see this from the days of Judge Landis to Congressional exemptions for sports leagues to judicial actions on free agency (Curt Flood), gambling, and property rights.
So while this type of controversy/disagreement has roots in the constitution, the NCAA and college sports environment reflects the challenges that the three branches of government encounter in attempting to clarify and apply "law"(in the Hayekian sense) in a dynamic society. The creative destruction in a liberal order leads to these tensions. The alternative to a dynamic society is terrifying for us and our grandkids.
@TheFarmFan points out the complexity of the process as the three branches interact in response to a changing economics, political and entertainment environments. The issue of state involvement in society is a contested one that defies simple advocacy. The economics and law movement in the 1970s initially offered promise in resolving some of these tensions, but unsurprisingly, has contributed to the conflict
50 years ago, has one considered legal gambling on sport (Pete Rose is rolling his eyes) with media sites promoting and benefitting, Las Vegas as a site for sports events, and the integration of these elements organizationally, you would have been called crazy.