So, the epiphany to have here, is that for many countries — but not the US! — historical cultural sites and artefacts (not just museums, but also things like monuments and land features) are a large draw for
foreign tourists. People fly to Paris
just to visit the Louvre; people visit Egypt
just to see the pyramids; etc.
These "historied" cities have built up powerful hospitality industries around foreign visitors there to see historical cultural sites. Insofar as you can think of a municipal government as "a dozen neighbourhood business associations in a trenchcoat", hospitality-focused cities like this have strong incentives to put large amounts of public funding into museums, art galleries, etc. — both just to ensure that these things are very nice to visit and continue to draw tourists; but even more, to reduce the costs to tourists of visiting those sites in particular as much as possible... as a loss leader to draw those tourists into the rest of the city, where the hospitality-focused businesses can then capture their money!
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But, why doesn't this happen in the US? Well, it's no one single thing.
• The US is big. There's a lot of stuff in the US, but you can't see all of it on one vacation. The "draw power" of any one US city to foreign "cultural tourism" is diluted because you can't just go to one or two cities and see all the cool stuff.
• In fact, many of the most "tourist-driven" sites in the US — Niagra Falls, the Elvis museum, etc — aren't in cities that people have any other reason to visit. All there is there is the site itself, and the hospitality businesses, with no other reason to be there. Because of that, people who e.g. travel for business, can't sneakily justify a vacation to these places by holding a conference or retreat there; there's no "there" there to make that practical, let alone enjoyable. They're just tourist traps, that you have to go a long way out of your way to visit. (The one exception being Las Vegas, a tourist trap so overgrown that you can hold conferences there — but it's hard to justify a "business retreat to Vegas" for other reasons.)
• And a lot of the other well-known stuff — the Grand Canyon, Mt. Rushmore, Yellowstone, etc — are (or are in) national parks, i.e. places excluded from capitalist build-up. Which is good insofar as it prevents a tourist trap; but bad insofar as it prevents these places becoming genuine hospitality-focused cities!
This is all very much unlike most of the rest of the world, where the big cities and the "stuff people want to see" are mostly co-located.
• Also, re: art and museums specifically — some might suggest that the US has nothing that foreign tourists want to see because "it's too young to have culture", but that's not true at all (see: e.g. MoMA; the Smithsonian.) I think the real "problem" with US museums is that they're modern in a way that means that all the coolest stuff can be seen in online catalogues; is well documented in video documentaries; etc. Meanwhile, other galleries and museums are old and crusty and not hip to technology (save for archival-science technology), in a way that means that you have to go there if you want to see it.