Sorry for the necro, but as I appreciate fashion-related PODs, this is interesting.
My own guess is that, with pantyhoses non-existant or not prevalent, we'd see a lot more women with skirts wearing either
tights or more old-fashioned
stockings during colder weather. Linen, wool, silk and lisle stockings would probably be still in fashion a lot more than nylon stockings/pantyhose, due to a lack of other choices.
I think your question requires some elaboration: Why would pantyhoses not be invented ? Is it due to a lack of the OTL material for their production, or due to something else ?