Even ignoring all the overhead that would bring, it's not feasible for a local municipality to do background checks on the net income or wealth of foreign visitors in any way that would be reliable. It would be trivial to bypass this with fake statements.
So then rich people will pay poor people to buy the tickets for them. And that's if you can come up with a way for someone to declare their wealth reliably.
The burden of oversight for determining income would probably wash out any gains made from taxing higher income people.
When I went to Victoria Falls national park on Zimbabwe, the fees were based on which country’s passport you were presenting. Richer country passport holders had to pay more, poorer country passport holders paid less.
That's not a bad idea!
Like traffic fines in some European countries, but with a lottery system as well if the number of potential visitors is high enough, with no substitution of people to eliminate reseller market for lottery. Some national parks in the USA already have to limit visitors and state and county and local parks in California that I have seen during the pandemic had to put limits on people visiting and a lot of that was free. Most of the US solutions are based on first come first served or reservations with first come first served so equity of any kind is not addressed otherwise.