The main problem with "separate but equal" in terms of segregation is that it was a lie. If you have separate but equal laws, as ridiculous as that is, it's functionally just.
Bathrooms? Seems like people like the way it is pretty universally. If you eliminate men's/women's rooms, you'd have to install more toilets in the unisex rooms, so it wouldn't save much on future buildings and would be an added cost to all current buildings.
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Weird. Creepy!