Some aspects of grammar are important, but it's important to reflect on the purpose of its study: The ability to construct a sentence that's cogent, clear and understandable both in writing and while speaking.
Some things are simply not important to know as a native speaker but still manage to get taught in English classes. A couple of examples:
1. The different between "that" and "which" (e.g. The curtains that/which cover the windows). Either way is perfectly clear and rigid adherence to a correct "rule" is just language fascism.
2. Terminology for many things that are specific to grammar are also pretty useless. Words like 'participle', 'split-infinitive', and 'gerund' (I literally had to look that up to remember it) are basically useless. Specifically from the test are phrases which obviously have been taught within the class, but don't have any real meaning outside of the concept it's teaching: "Parts of Speech" and "Define Case".
Grammar is only important insomuch as you can write and speak intelligently and coherently. Construction beyond that belongs in a linguistics class specifically focused on the mechanics of language.
