I know the Spanish case. The hotel lobby does not only push for airbnb restrictions but also for banning new hotels (so that they can push prices up). For example famously there are no new airbnb or hotel licenses since more than 10 years and obviously the problem has only worsened. Regardless, the problem is in general still a demand that grows roughly at 2.5x the supply growth rate.

Are the boulevards, museums, parks etc growing as well? If not, why should the number of hotels grow? A city generally has a limited capacity for tourism (one which is not primarily related to the number of hotel rooms) and once that is reached, it becomes detrimental to increase tourist accommodations. I don't know if this is the specific case in one specific city that you have in mind, but the principle is there - expanding tourist accommodations is not a good in and of itself. Supply is naturally constrained, regardless of demand, for many real goods, and this is one of them.

Additionally, you keep ignoring the fact that even if new housing supply would be very important, Airbnb is still a drain. If demand was outpacing supply 2.5x before Airbnb, and it's outpacing it 3x now, that is still Airbnb making a bad problem worse.