Since PCOS is one of the signs of insulin-resistance in women, a ketogenic diet is a great treatment for it. It’s so effective, in fact, that when I joined the forums in 2017, there were lots of jokes about “keto babies” and warnings to be careful, if you weren’t prepared to have a kid just yet.
As for the issue of baldness, I always assumed I’d end up bald, like my maternal grandfather (back in the day, it was supposed to be your maternal grandfather that determined your baldness), but it never happened. And yet, in the years I’ve been eating a ketogenic diet, my hairline has receded more than in the decade or two before. So I’d believe it does have something to do with testosterone.
PCOS and testosterone levels are another great reason for not worrying about having lots of cholesterol, by the way. Progesterone and testosterone are both made from cholesterol.