Honestly no idea why they do/did the home visit but what is really nice it that now when I see one of the policewomen around the town, she always stops for a chat!!!
We were visited for normal naturalisation - they rang and asked if we could be around the next morning and came along. It was very pleasant. They literally just chatted with us - asked a lot about the UK because one of them were thinking of going on holiday there! and left behind pencils, pens and stick it notes for the kids with the police logo on.
I wasn't visited at home, but in my police interview I was asked whether I work in a red light district. The officer said sorry, he had to ask - it was on the required list of questions. Neighbor ladies have reported also being asked.
It is, but pimping is not. I've never known anyone who said yes to the first question. I always wondered whether there was a follow-up if the answer was yes.
No, it’s not illegal. Zurich has had it’s own brothel in Wolishofen for many years, https://petite-fleur-zh.ch/
FWIW our local police just phoned, spoke to me for 3 or 4 minutes then OH for about 10. The fact he knew my OH probably helped!
Phrasing of the OP makes me wonder if there's something relevant we are not being told here...