Moreover, contrary to the assumptions of the present system, it's impossible to select good teachers by formalized bureaucratic and credentialist procedures.

Full agreement

Their ability is simply not amenable to formal bureaucratic evaluation, certainly not in a way that would be immune to Goodhart's law.

We could at least use a metric that's resistant to gaming, or that would provide useful data even when gamed, like using formal tests regularly, and comparing the progress of the classes a particular teacher tought against the average.