You have selected the wrong target. The problem with public schools rests solely on the administration starting with the principles, through the county school boards, and then the state's agency. Teachers must either follow the mandates of the "system" or find another job.
In those states where teachers are allowed to strike, the ruckus is always more than issues related to pay. Teachers have no other way to redress grievances with the school board.
Think of this: I asked why teachers are not allowed to bear arms at school on behalf of the students. The answer was "The fear that students would over-power the teachers in or to seize those weapons".
Perhaps you don't understand what is actually going on inside schools.
What Teachers' Unions Bargain For
Unions negotiate on behalf of their members for better compensation, but they also handle grievances; provide training; lobby federal and state lawmakers; and work to improve education quality for the students (such as reducing class sizes and improving curriculum). Unions may collectively bargain on behalf of teachers for a variety of reasons, including (but not limited to) the following:
Academic freedom; curriculum
Wages; benefits
Hours; workload; responsibilities
Tenure; promotion
Evaluation procedures
Grievance procedures
Retirement and pension benefits
Vacation and sick leave
There was a teacher on Andrew Wilkow's radio show on the Patriot channel who said that unions (she was speaking mainly of the NEA - the union most teachers belong to or belonged to before Janus) are the main force behind pushing the homosexual/permissive sex education in our schools across the country. Granted the curriculum are decided on at many levels from Federal through local, and principals play a role too, but a rather small role. But she said the unions are so powerful that they can throw their weight (they have enormous power) around and have a major influence on the curriculum as well. Which is why you see in this in a majority of the schools throughout the country.
That show & listening to her is what I am going by mostly.