Grammar rules are inferred from usage, not vice versa. Grammarians study language in use, relationships between words are observed, and structures and patterns come to be recognized, accepted, and then taught. For a beginner the rules are relatively unproblematic. Sure, they might conflict with one's native language and represent at times radically different ways of conceptualizing reality, but they can be learned.
If a student doesn't have "the Mary" sorted out, then that needs to be addressed. The rule that a name can't be preceded by a definite article is not only definitive but also easy to assimilate, so it's not something a little continued drilling won't be able to iron out. Grammar as we've traditionally known it is, in fact, indispensable - up to a point. One needs it to get one's bearings. But then there has to be a shift from an emphasis on 'grammar' as pattern to grammar as word group.
The problem with relying too much and too long on 'grammar' as a point of reference lies in its reductionism. John Sinclair writes that "grammatical generalizations do not rest on a rigid foundation, but are an accumulation of the patterns of hundreds of individual words and phrases," which I think is significant because so many of the words you go to teach students can only be used in conjunction with certain words but not others.
I recently wrote "make research" on the whiteboard and asked a group of higher level students if this was okay. Over half of them had no problem with it. Of the remaining students, one half felt it was wrong only because they'd never seen that combination before, and the other half knew that you "do research", "conduct research", etc. If as a second language learner you use only words and 'grammar' (in this case verb plus object) to express your meaning you could be right, but there yet stands a very strong possibility that you could be wrong.
This is why I favor emphasizing to students that there are things that you *would* say as opposed to things you *could* say. I think that as a student's education progresses, this move from the general to the specific will be inevitable.