Or do Japanese: There are two main types; the one where you and everyone else neatly follows the immutable rules which you speak to superiors and to strangers by default, and the one where everyone blurts out whatever words in whatever order they come up in their brain, aka what's spoken between friends and to acquainted inferiors
That's correct, 敬語 perfectly follows the rules, but while there are rules for 普通体 (ある instead of あります), people mostly just talk in whatever way they want that does not follow any rules.
It's quite shocking to me as a Dutch person, we hardly have such a big difference between formal and informal Dutch