I agree it shouldn't be a minister. It should be plain common sense and in straightforward policy.
However, as we will have a change in political majority at some time, going this route means whoever is going to have to make the decision cannot duck it. There's no hiding behind excuses. If a future decision is made to house males with females, that politician will have to own it.
Given the radio silence from the Labour frontbench on recent other developments (GIDS), I wonder if they would do it. I wonder if anyone would have this squarely at their door.