Maybe a lottery system then? 5k free "tourist visas" per year, that sort of thing.
Interesting position. Competing against that thought you have stuff like United Nations Universal Declaration of Human Rights #13: Freedom to Move. "We all have the right to go where we want in our own country and to travel as we wish"
The kind of restriction on tourism we're discussing here appears to run contrary to that particular line. Even at it's most conservative reading it seems to set the bar at 'if you're a citizen of a country then you can travel freely to any public place within it'. The idea of locking down a city to prevent that is exactly what's being proposed here.
Or are we talking about only international tourism here?
The UN charter is specifically about citizens not foreigners. Additionally they are talking about no militay checkpoints, preventing a marginalized ethnic group from traveling from point A to point B, etc. It isn't about not charging rich Americans a little bit more because they want to see New Zealand.
A lottery of some form might work, if prices are kept reasonable.
Suddenly, I'm having flashes of California, particularly SF, residential problems, including the hated NIMBY-ism.
Keeping the price artificially low would be like the policy of the old socialistic ideologies.
Isn't that what the free market evangelism teaches? As there is only one Venice, I would hope that the price reflects the amount of demand as well as the the amount of externalities that the tourism is producing.
This last aspect should be covered by taxes to ensure that the tourism not harms the city/environment, as not to fall into the trap of the tragedy of the commons.
Taxes are the definition of market distortion. It would be a crying shame if all the world's greatest sights were restricted to the rich due to government interference.
EDIT: It would also be a shame if all the world's greatest sights were destroyed by mass-tourism, so who knows? But pretending it's as simple as an Econ 101 problem would be naive.
Lottery or some other system to limit access could also work.