This essay is an interesting look into the importance of learning grammar. In summary, learning grammar is all about developing the ability to convey ideas without ambiguity from abstractions in our minds to words that can be read by others. Furthermore, the reason for language's complex constructions is that they are necessary to explain complex relationships.

One thing about grammar that is rarely brought up in the classroom is that the process of writing is not for the writer, but for the reader; improper sentence construction can be confusing and distracting. So, do your readers a favour and make sure that they spend their time thinking about your ideas rather than trying to extricate your meaning. Now, I'm not for linguistic prescriptivism, but playing the descriptivist card is no excuse for poor grammar. Again, the rules are there for your readers. You must match your writings with the standard grammar of your audience so that they can understand you.

By the way, the argument that grammar and logic are linked reminds me of the trivium system.

Link: Why Good Grammar? by Richard Mitchell