Also - if it is impossible to detect bad teachers, then it is impossible to hire good teachers and therefore they are hiring at random. And parental choice can't be worse than random or that would be a signal we could use to pick the best teachers.
I will give you that teachers know who the other bad teachers are.
Unless teachers happen to spend their days sitting around in other teachers' classrooms, I highly doubt that's the case.
Teaching is not collaborative work, and I would not be comfortable giving a peer review to someone who I never interacted with, outside my lunch break.
They do, however, have a pretty good idea of which other teachers they personally don't like.
This feels like an assumption to me.
My wife is a public school teacher. There has always been heavy collaboration between her and her colleagues, even more so now with remote learning. There are certainly unmotivated and lazy teachers and the other teachers know who they are.
Parents are on average stupid. So are government officials. Centralising the power just means that when there is a bad official, everyone suffers. Just because the best alternative is still bad doesn't mean there is a great option here. All the choices have drawbacks.