To be fair, there's really no rational justification for why the 23rd Century Starfleet would create such blatantly sexist uniforms, especially given the embrace of sexual egalitarianism that our society has made in real life in the decades since TOS was produced.
But in the 1960s, miniskirts weren't seen as sexist, but progressive and liberated. Previously, women's sexuality had been kept hidden away and women were expected to be so demure and scandalized by anything remotely sexual that they basically had no power over their bodies at all. Part of the sexual revolution in the late '60s had to do with women embracing their own sexuality, choosing to express it actively rather than being passive and overwhelmed in sexual interactions. Yes, they were still defined as sexual creatures, but they made their sexuality something under their own control, something they pursued for their own pleasure, when before the men did all the pursuing and controlling.
Remember, the push to put the women in miniskirts didn't come from Roddenberry or some chauvinist-pig executive. It came from Grace Lee Whitney. She wanted
to wear a miniskirt and go-go boots. I think it was Nichelle Nichols's preference as well.
Maybe in the 23rd century, the fashions happened to be similar to those of the 1960s. Maybe it wasn't seen as sexist at all for women to wear short skirts (or actually mini-culottes). After all, that's the era of IDIC. They recognize that two groups do not have to be identical to be equal. So if women of the era choose to express their gender identity as distinct from men's, that doesn't have to mean the society sees one as superior to the other.
So the only question is whether there's a major practical problem with that uniform design. Are there fundamental drawbacks? Perhaps; the exposed skin would be more vulnerable to sparks from damaged equipment or the like (although the women do generally wear hose, which might be made of some very durable 23rd-century material). And both sexes' uniforms are equally impractical in their lack of pockets.
TNG tried to take the gender out of it by putting some male crewmembers in "skant" (skirt-pant) uniforms that were essentially a unisex equivalent of the old mini-culottes. But TV viewers were too mired in their own 20th-century gendered assumptions about fashion and found it silly. (And really, why must the solution to sexism be to make women's clothing more like men's? Why is it okay to put a woman in pants but ridiculous to put a man in a skirt? Isn't that just a deeper layer of sexism, assuming that the male way is automatically the better one? At least TNG made an attempt to meet in the middle.)