That’s not really a consideration to the state governments deciding on how and why to keep teachers pay low. A version of that is at play in circulum design, but not really in pay.
It’s mostly a mix of:
Hatred of public schools
Their kids go to private, or well funded public districts
Poor resource management within state budget
Desire to weaken public education system overall, to advance vouchers, charters, etc.
Power. Getting off on their raw exercise or power.
The people who designed the system decades ago might have had the more nuanced, if still evil, approach that you outlined, but not now. The current crop are a lot stupider and their conception of cause and effect is a simplistic version of 1-1=0.