Interestingly, 'villages of people with wildly different customs and traditions going back 1500-2000 years' is basically the opposite of what's meant by 'diversity' today, which is a high population of newly arrived immigrants.

The former exists precisely because people historically didn't mingle much.

The diversity of the US is largely imported, througout it's history starting from the first colonists, the US didn't have that much time to create it's own, cultural diversity to the extend that europe has yet.

I don't think most people would qualify diversity as "lots of newly arrived immigrants", even those who champion diversity, they'll likely get closer to "people from lots of different life experiences".

I think the term is generally used to refer to a melting pot of cultures as opposed to a bunch of adjacent monocultures.

I'm not passing judgement on either.

Europe isn't really a monoculture or a set of monocultures either. Over it's entire history, cultures have mixed and seperated all the time. I don't think the "melting pot of cultures" is any different here than in the US other than the US has less history with it.

It's different because in Europe you have people whose ancestors have lived in the same village for hundreds or thousands of years. They walk the land where their language was invented.

Maybe their ancestors aren't really as pure as they think, but it's still fundamentally different from a country where everyone is an immigrant within the last few generations.

People didn't really stay in the same village all the time, there is plenty of mixing going on in history. Languages have moved as well, the german-french border can write you a long essay about that.

Considering the current political climate in the US, the difference isn't that large...

It's a different kind of diversity. But Europe has plenty of ethnic diversity too. If you were to believe American right-wing pundits (you shouldn't) we're being overrun by Muslim immigrants here. That's an exaggeration of course, but there are many European countries with significant numbers of immigrants and expats from all over the world. Amsterdam, not New York, is the city hosting the largest number of nationalities in the world.

I'm born and raised in Europe.

If you were, which I doubt, I would assume you didn't move around much or went to vacations in and around Europe. I would recommend doing that at some point, it's lovely.