I take the point (although I'd admit to being surprised if male prisons had a majority of female staff). For me, I think it's a (set of) cultural issues, take schools for example, you are absolutely right that for primary education male role models are basically absent. In mixed secondary education, it is almost reversed. The same is true in volunteering, as a man, it's way easier to volunteer to work with teenagers, as I currently do than it was to volunteer to work with small kids.
Maybe I'm wrong, but I suspect an overwhelming majority of parents here would be much happier with a female babysitter than a male. I'd expect the same to a lesser extent about reception/year1 teachers. This is, absolutely, partly risk - but I think it also speaks to a deep society-wide cultural view of women as for example "nurturers" and caring men as inherently risky and 'unnatural'.
I feel that this has become worse over the years, rather than better, I'm a GenXer and I find the idea of an Andrew Tate in the 1980s simply unimaginable. We obviously had horribly misogynistic men then, but even then the idea that explicitly, rather than implicitly, exploiting women was a desirable and profitable goal was crazy.
Somewhere along the line the conversation seems to have become one where equality is not a common goal, but at least for some a cultural divide - I might compare racial equality at this point as well. It is hard for those in privileged positions (sex, wealth, age, race, attractiveness, ability) to even see the privilege, let alone engage with it, and we seem for good reasons to have decided that the struggle is only for those on the wrong end of the power relationship.
P.S. it's now a quarter past midnight, I hope this isn't as incoherent in the a.m. as I fear it might be.