Most hotels in Italy seem to ask for your passport and most want to keep it overnight. (I believe that they are required to register guests with the police.) I ask if they cannot take down the details while I wait, and on all but one occasion they have done so. On the other occasion (which I think was at a tourist hotel in Venice), they said no, so I called at the front desk again about half an hour later and asked again, and they reluctantly replied (presumably thinking that if they didn't do so I'd be pestering them all night!).

Two things worry me: one is that they'll lose the passport or hand it back to the wrong person by mistake. The other is that in many European countries one is required to have official ID on one's person at all times, and although the regulation is rarely enforced (and moreover, in any case, a reply from an obvious visitor that the passport was at front desk of the hotel would probably forestall any real difficulties), it is sometimes invoked.

I would certainly object most strongly, and probably check out, if a hotel wanted to keep my passport for the duration of the stay.