The way I see it the main problem for women to see prizus is that seeing someone who is oyver aveira has bad influence on your ruchnius (this is the main problem I could think of). This is not a problem in the swimming pool where there is no aveyra to begin with. That’s pretty obvious.
With that said, saying that it’s the same chumra for men and women, or that it’s worse for women, seems completely crazy (the idea not the people) because for men histaklus leads to hirhur (?????) and maase (????) So I’m sorry but it makes no sense.
LU I think you would agree with me yourself if you knew what a big deal they made of shmirat aeinaim in the yeshivos, as opposed to how little they talk about it in seminaries.