But you're comparing exceptional teachers to average doctors/lawyers. The people that could be great teachers have a lot of good alternatives, so if you want good teachers to teach, you need to reduce their opportunity cost by paying more.
Then you have to ask yourself should these great teachers be teaching average students, or should they only be teaching the best? Or should they be incentivised into going into science or engineering? These are tough questions, I honestly think the best scenario would be for top engineers and scientists (practicing) to mentor students, and help them see the big picture/inspire them while their teachers train them in the skills necessary.
But teachers pay is only a function of seniority. The system doesn't care whether a teacher is good or bad, the pay's the same if they've been in the job as long.
Most people simply do not want to work in an environment like that.
