And that is free market at it's best. If something is in high demand with limited availability then I would expect the price to rise.

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.