Yes, nearly every country I go to that isn’t next to the border does.
Even Canada asked for it.
In Mexico though, they report like they do in China.
They let the authorities know “so and so” is here at our hotel.
I am sure if you go to a flea bag hotel though, they won’t report you. Those places don’t even have sheets on their beds so why would they even bother.
Yep. Some countries where I have visited require that you surrender your passport when you register at a hotel (that is why I always kept a clear photocopy of the information page of my passport with me at all times).