Here’s a long, detailed article in the New York Times Sunday Review, “Is it time to desegregate the sexes?”
Primitive societies often do.
I’ll add this thought. Sexes are generally kept separated when fully nude to make adult sexuality (usually heterosexual) more fulfilling when it eventually happens in appropriate circumstances. It’s more than just “privacy” (as we saw the idea thrown around in 1993 regarding gays in the military). I grew up in a culture that, at a certain level, valued female “beauty” more than male (as opposed to nature – like with many birds). I found it interesting when partial “revelation” showed some men to be more “manly” than others as they grew up, and the same can be said about women (especially by Donald Trump). But for an attractive male to show off in public seems noteworthy.
Still, as a nation and in our particular communities, we have more pressing concerns than the bathroom bills.