When you underpay teachers, people who hate teaching, and hate being teachers, will become teachers because all the people that had better options did something else.

Yeah, why would we pay top dollar for top talent and then hold that talent to high standards? That certainly doesn’t work in any other profession.

When you overpay CEOs, people who hate leading, and hate being CEOs, will become CEOs for the money.

Is a good idea to select the people who hate leading to become CEOs?

This is true of every single job.

Teachers are high in big five trait agreeableness which means they typically don't negotiate on their own behalf

Absolutely dumb take. There are plenty of very bright and talented people that would have made excellent teachers but chose different career paths because - surprise surprise - the pay is better.

You made an assertion that is based in fantasy, and then asked a question based on this silly assertion. Just wow.