IMO, this tax/fee will have zero effect on the amount of people visiting, as it's a drop in the bucket with respect to total travel costs. So as a deterrent it has no significance. It can be a useful source of revenue to offset some of the negative impacts that the many tourists have on infrastructure, etc., if used wisely (and not lost, say, in bureaucratic mazes). And you can't raise the fee very much, because that would not be fair to tourists who are less well off.
If destinations like this are indeed bent on lowering the amount of tourists - and I'm not sure they are - then the only realistic option today is to limit the amount of time a tourist can spend in them, or restrict the flow in other ways. This, for sure, raises other questions, but I think it should be seriously considered.
Solutions that involve the use of "smart" management of infrastructures and movement of people are still on the drawing board, and I don't believe they can make more than cosmetic improvements. Crowds are crowds, travel is on the rise, and old cities are just that.
In the end it will all come down to personal choices. Those of us who have only experienced a popular destination while being surrounded by throngs of foreigners like himself, and have found sufficient pleasure while doing so, will continue to other destinations like this. Others will cross them, with regrets or not, off their list.
The locals will also have to make their choices, some embracing the situation, and some, like we have seen, clearly showing their discontent by (for example) displaying banners or posters deploring tourists who use AirBnB in their city.