I'm not saying that public health and safety couldn't do this - I'm not even saying they shouldn't. I just find it incredibly disingenuous to assume that only a public institution could conceivably perform this function.

Btw. regarding your argument that brothels could be regulated under local planning authorities - I'm pretty sure that's exactly what the OP was talking about. We just got side-tracked by the minor point of who gets to do the H&S.