I don't remember diagramming sentences until I was in 6th or 7th grade. We did "how to write a paper" in 5th, and then it came up when we needed to write one (which was rare). I was a debater in high school, so practiced organizing my thoughts in that, but it wasn't needed in English classes.
I never needed the grammar practice, because my mother was a prescriptive grammarian who corrected me every single time I said something the wrong way. So proper grammar was always what sounded right to me, whereas it sounded wrong to many of my classmates.
A foreign language with more inflections / cases than English uses is a good way to understand English grammar, too. I don't remember how it came up, but I found myself teaching DD a bit of German over the weekend to explain some aspect of English grammar. Although I think I was good at German grammar in large part because I was good at English grammar.
DD is learning about as much grammar in 3rd as I remember having been formally taught at that age. They're working on quotation marks at the moment, from what she's bringing home. And have covered nouns (common and proper), subject and object of a sentence, and pronouns.
