Consider a world in which every female wears a short skirt
This is already problematic. Why, exactly, does every female wear a short skirt?
If they go to school in Tokyo? I mean, a lot of anime is based on schools and Tokyo is the nation's most prominent city. So it makes sense that even the anime set in fictional cities take a big part of their inspiration from the capitol.
but also overacts everything and as such physical movements are super exaggerated. Seeing panties occasionally is a natural result of physics in that situation.
This sounds like a situation specifically set up so the viewers can see panties, which isn't natural at all.
(Edit: Well, it might be natural in-universe, but it's certainly deliberate out-of-universe, and both must be taken into account. No piece of media exists in a vacuum, after all.)
It's prevalent for reasons pertaining to the nature of anime in general, certainly. But nothing I mentioned is specific to fan service heavy shows, or even shows with adult or male audiences. Hell, it's more common to physically exaggerate things in kid shows.
As for the "they always were short skirts so it is inevitably sexy" doesn't really hold up that well, because there is no "well that's how it is" that isn't in the creator's direct control. It's not like the Grammy Awards where there is a wardrobe malfunction and you see tiddy and you go "well those things just happen sometimes", everything in fiction, especially animation has been carefully scripted down to the last single frame.
Yeah, but at some point art has to follow reality. Barring cultural sensibilities that inspire censorship, there's no reason to specifically bar underwear from appearing in a show. If your concept calls for a girl to be recognizably school-aged, that means a skirt, and (given Tokyo's media dominance) probably a short one. And if your concept calls for fighting, sports, or even pratfalls, there's probably going to be cases where the skirt is in a position other than hanging demurely at the character's side.
While I do enjoy a lot of series that have fanservice, I think that there's really no excuse for rationalizing things as "natural". In fact if it feels that natural that implies that the decision to include fanservice was made at a more "meta" level, e.g. it's been designed in as a more pervasive thing. e.g. if the "sexy shot" is a specific sequence, e.g. a shower scene, then that's the decision to create one a sexy scene in a sequence. Whereas if it's "all the girls in this show wear ultra-short miniskirts", well that's a decision for the fanservice to pervade every pore of the show's existence.
Something like "the main character makes clothes explode" is almost certainly going to be for titillation. I can conceive of other possibilities, but none that would actually get an anime. But something that shows more skin than your culture likes isn't necessarily going to be just about sex appeal by default. You can call it a meta-decision, but I think more often it's a non-decision. The studio goes with the default to their culture or industry, without necessarily going into the why or if too deeply, simply because this isn't related to the vision or original work, and thus is an ancillary detail.
That's without getting into differences in cultural perspectives on nudity. Where the west sees it as inherently sexual, the East sees it more heavily as embarrassing, and we see it used comedically more, or to signify that a character lacks propriety and dignity in an entirely non-sexual way, like with Aqua in KonoSuba. But that's a whole nother kettle of fish.