How come EU doesn't care for something that so unnecessary pollutes, driving millions of people from big cities to tiny places that clearly can't sustain them? Well , too many european countries rely on tourism, that's it.
But if you sell them it automatically becomes a form of classism (advantaging the rich while penalizing the poor).
We could institute a "tourist license" with a three to six month course on the history of the destination and respect of basic rules of behaviour, with a final exam to get the license.
But again that would be discriminatory, some way or the other.
We could impose the need of a (licensed) guide/assistant for any tourist or group of tourists up to 5 people, but then again that would favour the rich.
So, the only way would be a lottery of sorts (but then you would have to carve the exceptions for those traveling for business, for medical reasons, for studying, for x, and y).
Then you would have to find a way to check these tickets, some procedures for when these tickets are lost or stolen, etc., a sure way to cash fines when people is found without ticket or breaks any rule [1] (an advance deposit of US$ 5,000 or € 5,000 on an escrow service would nicely do, but again the rich will be favoured) .
Then, obviously, you cannot have the same treatment for citizens belinging to EU countries and the rest, so the total allowance should have a quota reserved to our EU neighbours and a separate one for those countries that are "friends" and require no Visa, before "the rest".
Seems to me like a dream that EU bureaucrats, bankers and IT firms can have.
[1] you will need also some new Laws and Courts to manage the oppositions to the fines
May be, you should divide your town to public (tourist) place and non-public place, where tourists enter severe limited.
Some want to relax in pleasant weather with beautiful scenery. If their hometown climate sucks thry're always going to move to the right weather zone, but with good infrastructure they could theoretically be better spread out so they don't overcrowd the same beaches and mountains in the same countries.
Some want to party in such places. This is slightly different because they want to be in a crowd, and they don't mix well with other types of tourists (let alone locals). But good marketing can lead them towards dedicated "party villages" away from other people to have their fun.
Some want to see new places. This is where I think an education campaign has the most potential: my experience is that well-rounded people are less impressed by a trip to Paris than by a trip to some fascinating destination that their peers have barely heard of.
And some, unfortunately, do desire to specifically see Venice or the Galapagos or some other place that cannot host all of them forever. A gate mechanism is needed, and frankly a monetary gate is the only remotely reasonable one to implement.
They (the flock) don't actually know anything about where they are going to and they only go there because it is mentioned as "cool" (or whatever) on the internet.