I agree that this sounds like a different kind of voucher/private school resource transfer. Private schools are able to self-select their students and aren't required by law to take
ALL students that want to come. This makes it trivial to be both cheaper and show better test results while at the same time removing resources from the students that actually need help.
The problem is that people in power thinking that this is mostly a teacher driven problem. This would be the same approach as saying that a the amount of money a doctor gets paid should be based on how much weight their patient loses (e.g.) Anyone who thinks teaching is so easy should go try it for a month. This kind of approach also misaligns incentives. The fact is we have good teachers and bad teachers, just like every profession. We need to rethink two things for our education system. Is it to just push kids to college or is it to maximize the number of students who can become gainfully employed and self-supporting adults. Then we need to restructure our resources towards that goal, specifically in terms of class size and ability level and extra help. The main change we need to make is to move investment of resources much more towards elementary age where it can have the longest compounding benefit. (Source: I'm from a family of a dozen current and retired public school teachers)
I do agree that if we increase the pay and benefits for ALL teachers, then we'll create incentive to get better quality teachers in the profession and that competition will get better results in the long term.