Just because someone is a different ethnicity doesn't mean we don't have a shared culture. Immigrants move to a country because they like the language/culture and want to be a part of it.

Immigrants move to a country to take advantage of the opportunities there and improve their standard of living. I have never met an immigrant that moved to a foreign country because they "liked the language/culture and want to be part of it".

Then maybe the incentives are wrong? If I ever move to another country, I'll pick the country based on the culture, not just on opportunity. It's too important not to think about.

depends on the (source:target) pair. People immigrating from India->US are coming from a vastly different background/goals/needs than those going US->India. Money probably dramatically beats out culture wants until you reach a certain point; those coming from a first-world country likely have lower monetary wants, and so culture has greater relative value.

Those coming from third-world to first-world are likely much more interested in money than culture, and I can't say for certain but my intuition is that the kinds of ethnic segregation (eg in NY/Chicago, where there's a whole array of little microtowns) that you see in the US are mostly generated by those poorer populations seeking wealth, not cultural value.

I imagine the equivalent American/European expat towns don't exist nearly as strongly/commonly in india/china, as the inverse exists in the US. (of course, you'd also expect less americans/europeans migrating to india/china, since the monetary difference isn't as strong).

What you are saying is true, which is why a single national language is important. People will naturally gravitate towards communities where their language is spoken, so we unify ourselves by ensuring that English is the common national language.