It depends on where you are from. For instance, within the EU, there is a residence registration requirement that extends to temporary residences like hotels as well. For EU citizens, they just need some form of ID - but for people from other countries, they actually need their passports. So showing your passport/ID to a hotel clerk when checking in is something completely mundane and normal in the EU, as well as them asking for it even when you are already holding it out to them.