Why can’t we just have four separate jail departments and statistics?
They usually seem very reluctant to let stats out.
A cynic would suggest it's because they would show no tendency whatsoever for trans inmates to have opposite-sex offending behaviour.
There was some recent freedom-of-information success in the US which managed to determine that 50% of MtF prisoners in federal prison were convicted of sex offenses, compared to 4% of FtM.
And the total number of FtM prisoners is far smaller than the number of MtF, so that's much more than a 10:1 difference. (50% of the FtM in federal prison are for drug offenses).
Personally, I would actually be open to some suggestion that there might be a subset of males that somehow has "lady brains" such that they behave like females. I'm not philosophically against the possibility. It could conceivably happen. But you need to have evidence.
But all the actual empirical evidence - like prison stats - shows that it doesn't. Or at least if it does, the people calling themselves "transwomen" don't have that characteristic. They're very, very male-behaving. They would have to commit about 50 times fewer sex offenses than they actually do to convince me they're somehow "female gendered".