As far as logistics are concerned, we already have models for how many people can comfortably fit in say a theme park. Similar models exist for maximum population density in a city. If we were to use such models to estimate a maximum tourist capacity within a city, dependant on public space, transit and other infrastructure, we could find a very reasonable limit for tourist accomodations.

Either way, the decision to impelment such limits should be a democratic one, for the whole city. Private companies don't often care for the quality of life of the locals.

Change in a city is just as important as preservation imo, as long as the change is driven by the locals not a foreign for-profit actor. After all, at some point there's barely any of the original city left to visit.