That's true. As with all entertainers, the great wealth of MLB baseball players and the most touted amateur signees is in a way their dumb luck to have the income in their professions explode through the work of physicists, computer scientists and electrical engineers who wrought a communications revolution. Without that progress made in fields far removed from their own, athletes and actors would still be the low-paid troubadours they were a hundred years or more ago.
Today, in the real world, the money from sports and other entertainment goes either to the performers or to the owners/providers of capital. I prefer a larger share to go to the entertainers, who are the true producers of the product. It is hard to argue they are overpaid, from an economic perspective, because they are in a business where the $ product of their labor is directly measurable and is ponied up by individual consumers. So, in good capitalist fashion, we can say that consumers have made a collective decision that the utility to them of baseball games followed in-person or by TV, radio, or internet and the owning of baseball clothing and other paraphernalia is worth an aggregate of $X. The two questions to be answered are:1) how are these $ to be split between owners and players; and 2)from a team perspective, where are the $ for player salaries and bonuses most efficiently spent. $ spent on draft and international bonuses, $ spent on young players are both worth a lot more than $ spent on older vets (at the salaries older vets commanded arguably up to a year or two ago or perhaps still command).
Teachers are in a difficult situation. They are in one of the few professions(education in general) for which long-term productivity has been negative. Regulation plays a big part in this problem, but so does the tendency of educational organizations to drift toward an ever higher ratio of (non-teaching staff)/(teaching staff). The number of students whom each teacher teaches has gone up and down, but over the past 60 years is down. For colleges, the federal and state governments tried to help by providing scholarships/loans to students and direct aid to state-affiliated colleges. Colleges responded by slurping up the $, leaving students to pay as much or more as before, with the extra $ going to bloat, increased amenities, responding to regulators under a basically airline pricing method, in which the maximum $ are extracted from each family.
Teaching and baseball playing are both basically service industries, but the one has greatly benefited from new technology amping up productivity and the other has not.
It is also a different matter to say that education is vastly more valuable to society than baseball and to say that a particular given individual teacher is worth more than a baseball star. In the aggregate, vastly more money goes to education than goes to baseball, but education has vastly more employees.