Agreed, what we learn as "grammar" in school doesn't correspond to the real rules of the language we use - either because the "rules" taught are "wrong" (like "not splitting infinitives"), or they're teaching a different language from the one you learned at home - in fact, I suspect this last one is the main reason schools feature prominently teaching something that people learn naturally : it's part of an effort from central governments to impose a common language to the whole nation, instead of the local dialects that existed before widespread schooling. Teaching grammar rules explicitly makes sense if you're teaching a second language (which was the case for Welsh kids learning English, or Basque kids learning French).

here's a linguist writing about something similar:

The fact is that almost everything most educated Americans believe about English grammar is wrong. In part this is because of misconceptions concerning the facts. In part it is because hopeless descriptive classifications and antiquated theoretical assumptions doom all discussion to failure. Amazingly, almost nothing has changed in over a hundred years.

... though his conclusion seems to be "teach the correct rules of grammar at school", whereas mine is more "what's the point? People figure out the rules independently of what factoids they're forced to memorize in school".