Yes, accurate grammars are better than inaccurate grammars. But I think you are focusing too much on the negative effects and not noticing the positive effects. It is hard to notice people's understanding of grammar except when they make a mistake or correct someone else, both of which are generally negative effects.

Americans are generally not taught English grammar, but often are taught a foreign language, including grammar. Huge numbers of them claim that studying the foreign grammar helped them understand English grammar. Of course, they know the grammar is foreign, so they don't immediately impose it on English. But they start off knowing so little grammar that the overlap with the other language is already quite valuable, as are the abstractions involved.