Not quite true; sometimes, if an infection develops (even without a cavity, just because food got caught in the gums) it can be significantly more painful to deal with than getting it taken care of when they're healthy.
Of my 4 wisdom teeth, I got 2 removed for that reason. They got infected at least once per year un my twenties and it was really painful. Doctor never recommended to do it, but did tell me "if you feel like it's too annoying, we can remove them". I was the one asking after a holiday completely ruined (and no pharmacy available). So 2 it is.
Now, all good with the other 2,however the new dentist suggested removing them because those are a little bit extruded (they have been this way for a long time). Looks like I need a new dentist
Sure - it depends on the case, and that’s entirely my point. If it hasn’t erupted but still is, it may move teeth. If it has partially erupted it may be harder to clean, etc. My point is blanket “don’t worry until it’s infected” isn’t quite right either.