Not only that, but very few industries pay for their employees' education. Nobody paid me for mine though certain levels of education were a requirement for numerous positions I have had. Why should teachers' be any different?
Also there is very little room at the top in just about everything. There are only so many coaching positions in the NFL and all players will not aspire to or be qualified for those positions. There are only so many supervisory jobs, so many vice president positions, so many CEO jobs out there. We always hope the cream will rise to the top to be the CEOs and supervisors and principals and superintendents, and not all will qualify and not all who do qualify will want those kinds of jobs.
A republic that protects the unalienable rights of the people and respects human rights gives all who have the drive and ambition and ability to achieve whatever their hearts desire. But while it allows for the most free people on Earth, it does not provide all we want. And what we want in the way of wages, benefits, hours, and working conditions doesn't fall within the scope of unalienable rights. Sometimes its necessary to choose what sacrifices we are willing to make and what effort we are willing to put out to get what we want.
Coaches in the NFL get to pick the best of the best for their teams. Can you imagine if they were required to take ANYONE (including those who don't even want to play football) on their team? And at the end of the season, they are determined a success or a failure based on the end performance of each player on the team including those who rarely showed up for practice, refused to drill, and sat down on the field in a do-nothing pout when the ball was in play?
Well coming at it from a purely practical standpoint I don't think the schools should have to take anybody. I think schools should take the students who are capable of doing the work, who maintain a reasonable degree of civility, and who are not disruptive to other students or the school staff. If the community votes the funding, those incapable of doing a minimum level of work should be handled by special education. If there is insufficient demand for that, the parents would need to put together some kind of private system or home school.
It would be up to the parents to teach their kids the virtues of respect for other students and respect for authority. Those kids incapable of learning that should be expelled and the parents make other arrangements to educate them. The parents will make every effort to educate them until they are at least 16. No kid will be eligible for an unrestricted drivers' license, however, until he has achieved a highschool diploma or a G.E.D. or reached Age 21, whichever comes first. I think that would take care of a whole lot of motivation problems. Also if there is sufficient interest, a vocational school could be established for older kids who can't or won't cut it in the regular classroom.
Parents will also be responsible to see that their kids have a decent breakfast and lunch money and adequate school supplies (tablets, paper, pencils, crayons, etc. etc. as most of us were required to have.) Those that do not will receive a visit from social services. Except for the most unusual circumstances, parents who cannot or will not provide the barest basic necessities for their children should not be allowed to keep those children.
And meanwhile the parents will demand that the teachers teach real subjects and that their kids have opportunity to learn reading, writing, math, science, history, and social studies sufficiently to be educated and without ideological indoctrination. And if that involves busting some unions to get teachers who want to do that and who are good at it, so be it.