The head is eating the linguistic tail. ;-) Here in the US, we don’t experience “school” as infantalizing because school is as much for adults as for children.
Take our expression “night school,” which we uniformly receive as a phrase describing university or trade school classes held at night for adults who work during the day.
Or take the typical American phrase one asks of young adults. “Where do you go to school,” which is understood to mean university or other post high school endeavor.
Even conservatory is “school” for us.
I have to consciously try to remember when speaking to non Americans that school for them is something for children, because for us, that connotation is absent.
But now you’ve triggered the linguist geek in me. ;-)