And then you've changed the meaning of these pieces of cultural heritage to mean they are some kind of exclusive culture that can only be accessed by the wealthy bourgeois of the world. There would be no limit to this, they can artificially make the price as high as they want. It should be on a ticketing basis that is limited daily, not by pricing out wealth brackets in the world. You can only imagine that of the hundreds of thousands to millions that visit these places every year, there are millions more people that may never visit.
Those nice homes and cars have materials and resources invested into making them. The resources around tourist attractions are limited.
Well there's paintings that are part of our cultural heritage that most of us will never see, other than in reproductions. Doesn't mean you can't appreciate it. I don't really mind if the original is owned by some billionaire. The cultural significance is still something that's open to everyone to appreciate. But we get to do that knowing some guy who really cares about it is spending crazy money on maintaining it.
Not saying it's fantastic, but if you have to ration a resource willingness to pay is a place to start.
I don't feel the same way about every resource (eg health and education) but whether you can visit some old town somewhere doesn't seem essential.