I completely agree that teaching grammar by itself just does not work. I am old enough to remember being taught how to diagram sentences by nuns in grammar school and learning the rules of grammar at very young age. This no longer is done and our college students come to class with varying degrees of a grammar background. A first year writing class cannot fix all the problems.
We need to acknowledge that each class has some students who just want to slide by with a passing grade and others who really want to improve their writing for college and their future. Students who earnestly want to learn to write better appreciate learning more intricate rules. I introduce my entire class to the website Grammarbytes where they can work on their writing issues. The motivated students like the interaction and explanations.
There is nothing more discouraging than having a paper returned to students with marks all over pointing out the sentence errors. However, students need to know that one long string of words with no punctuation confuses the reader. I make a general comment at the end of paper.
I do think that students should be at least introduced to the rules of grammar as just like learning a sport, there are rules. Some students have it easier than others from their privileged upbringing. I would love to learn an easy way to integrate teaching the rules.