Assuming the tourists have more money than the locals and anyone can rent their apartment out to tourists instead of long-term to locals, you pretty quickly get

Assuming the tourists have more money than the locals and anyone can rent their apartment out to tourists instead of long-term to locals, you pretty quickly get to a point where "AirBnB-able" housing stock is taken off the actual housing market. This is a problem that can't be solved by building more housing, because that housing is not going to be built in the historic city centers where the tourists want to stay. (Also, it takes a while to build more housing.) Wouldn't the real market solution be to build more hotels?