What is the place of grammar in language teaching?

The pedant in me is alarmed:

Unless you want to sound like an uneducated backwoods hick, practicing proper grammar is incredibly important.

A lot of very smart people seem stupid because they can neither speak nor write well.
To master grammar is to master the details of the language. This sets you apart. As Mies van der Rohe said, God is in the details. He was right: Details are the difference between average performance and mastery.

I have nothing to add. You said it quite beautifully.

Teacher would tell that the sentence below is not correct, explain why it is not correct and show how to make it correct.

Teachers help motivated students navigate the difficulties of a subject, explain rules, give examples and provide feedback.
Just look at the questions asked on this forum. Much more than a half of them are about grammar.
Just from the first page: have or havn’t, Usage of ‘so much’; ‘so much as’, ‘as much’, ‘much as’; 50 yeasrs and 5 minutes; in spite of and despit of; Ready to download vs. ready to be downloaded?; Of who are you speaking? vs Of whom are you speaking?; Direct object or indirect object; Should I use swear-word or swear-words?; Doubling the last letter…

Some do learn by imitating, but not everybody is a parrot.

There are answers to all of those questions.None of us should stop trying to learn.

Thank you all very much you have all been very helpful. I would like to thank Milanya for all your help.

That was a great discussion, and a subject that I have also considered at times.
Thankfully the topic has petered out before blood was spilled, rather like arguements about politics and religion. Anyway, the whole point of this Forum is to help students with the problems that they are encountering in understanding their " teachers " teaching . Let’s get on with it.!!!