The subject of much debate and litigation, indeed.
The legal framework here, as I recall, is that sports leagues occupy a singular place in the business world. They are at once a group of competing entities (teams), and, of necessity, a legal monopoly (the league).
The draft is deemed a necessity of the league to thrive, hence it has been upheld by the courts until now.
My gut feeling is that your are off base on that, both legally and historically. I believe that the only basis by which courts have upheld the legality of a draft is that a players union had voluntarily entered into a collective bargaining agreement with a league and agreed to a "draft," thereby waiving its members' rights to contract freely as individuals. That is what a union collective bargaining agreement generally does.
People forget the historical fact that professional baseball leagues thrived (in general) without any "draft" until about 1965. Even today, there is no "draft" for FOREIGN players entering professional baseball - they can agree to play for any team they wish. Similarly, professional hockey did not start a "draft" until the 1970s(?) and was able to thrive before that. In fact, even professional football wa in business before it started the first sports "draft" c. 1935. Although it hardly "thrived" before then, its relatively unstable finances during that eatrly period can be attributed to factors other than the lack of a "draft." And college sports have always survived, if not thrived, without "drafts."
What is a necessity of a league of professional sports teams to thrive is that league members recognize contracts signed by players with other members and are barred from negotiating with such players until their contracts expire. This should not be confused with a "draft."