Solving the problem of over-tourism is different than raising the price of travel overall. When talking about over-tourism, we're only really talking about a few thousand places which attract so many tourists that they cannot function in a healthy place. If you increased the price of tourism in those select places, then yes, you might have the unfortunate outcome that only upper-middle-class people could visit Paris in May, but all those other people could go to smaller cities in central France which are still full of culture to experience, and might stand to benefit a lot from increased tourist revenue.

But maybe I am a bit biased because I like to visit obscure places anyway.