The melting pot, to some degree, eliminates that diversity, though. After a generation or two, lots of people are unable to speak their parents/grandparents native language. Perhaps that's less true today, with cheap travel, the internet, and people placing more value on diversity and knowing more than one language - it'd be interesting to see some research. Anecdotally, a ton of the older Italian-Americans I've met don't speak Italian much - they wanted to blend in and not be 'foreigners', and only later in life realized that not speaking the language was a loss.
When you look at a random central European city, and see Slovenes, Austrians, Turks, Albanians, Greeks, Serbs, Croats, Romanians, Germans, Russians, Poles, Italians, Macedonians, Bosnians, Ukranians, Moldovans, Estonians, Lithuanians, etc etc etc, do you think to yourself "Wow, there's no diversity at all here, is there? Everyone is white!" Then how about any random western European city, where you'll find the same mix, plus immigrants from their former colonies in Africa and Asia, plus the usual North Africans, does that almost meet your standards?
There are some very diverse countries in the world such as India, the Russian Federation, Indonesia, South Africa and DR Congo, all large (former) colonial empires in the old world. Some might even count the European Union, depending whether you think of it as a confederation or not. There is nothing like that in the Americas.
Given our peculiar history, yes, it means a lot.
[My impression was that in the days after the HK handover, it seemed like half of HK moved to Vancouver (I gather the Canadian government had unusually generous Visa policies), and that apparently really started a ball rolling; the last time I was there, it seemed amazingly diverse.]