This entire conversation is a bit silly, and might be drifting into areas too political for the main board. But to keep it focused on baseball, I will say that a few people here ought to make an effort to recalibrate how they think about such things.
In the first place, baseball is a government sanctioned and regulated monopoly. There is no magical free market of players deciding to form their own teams and build their own stadiums and schedule their own games. (And yes, as an aside that's what ownership does: advertising, providing a physical place to play, personnel management, staff, etc. I'm not saying other hypothetical stakeholders couldn't fulfill those functions, but it's a libertarian's child-like perspective to think the stadiums just pay their own taxes, and water-bills, and power bills, and insurance policies, and repair and repaint themselves.) Because it is a monopoly, the public has very little choice in who they are paying to see. Even post-internet.
In the second place, the societal regulator on all human activities has always been (from the days of the Pharaohs) - laws and taxes. Both the apples and the oranges are allowed to be grown, and a certain number of them get put back into the seed pile (either through private incentive, or direct governmental regulation.) So the idea of teaching (not free market) and sports figures (not free market) being very different is fundamentally odd to me. Perhaps it's partially fueled by the myth of meritocracy inherent in sports that we so much enjoy? That there's some universal aptitude testing for skill X and when we see excellence displayed in this particular game, it means some sort of true selection has taken place? (I mean putting aside the PED issue, there's multiple millions of kids who don't have meaningful access to the sport.)
In the third place, all money is public money.