Peer-reviewed publication is how scientists communicate with each other and keep track of errors
Depends on the field. It would be better if papers were more readily retracted when wrong. And peer review itself is a kind of group-think that sets the bar very high for hypothesis that go against the paradigm and prevents publication, for very Human reasons, of contrary analysis and opinion. Peer review isn't in itself all that useful a process for science.
Now if the school is State funded then that's a different matter. Otherwise, let them teach whatever they want.