It's not segregation it's settlement. If you moved from the Ukraine, Poland, wherever to the US, would you rather not live in areas where you can get the same things you had at home? Areas where "bilingual" means your language and English?
An integrated society does not have pockets of foreign cultures scattered through its geography, but it has a culture of its own influenced by all those foreign cultural inputs.
Well what you're describing I would call a society that has become homogenized, which also happens over time. And I think you are doing it because you're associating cultural areas with "segregation."
The Italian and German immigration waves are long over. We don't look as someone with the name "Schultz" as not being American any longer, however there are still ethnically German neighborhoods in major cities. Are you suggesting that we are still segregating Germans?
No, that's where the Germans live and their culture survives. No one is saying that they absolutely have to live there, and certainly not everyone that lives there are German. But its the area where German culture remains in abundance. And, in any major city there are still areas where those cultures survive.
Italians are Americans, there is little Italy, no one is going to see an Italian surname and assume that they aren't Americans because of it.
What you describe is not a society where people can choose to experience their heritage but a society where people feel they have to live in close proximity with other people with the same heritage in order to experience it.
German cuisine is totally removed from Mexican, from French, from Indian, from Chinese, you can see certain items dispersed to just about EVERY store in the US because we assimilate to immigrants as much as they do to us. But there is not a demand for arugula in every part of the country, same with chickpeas, not everyone is going to wear a chadri.
America is over 2,000 miles wide, that is a hell of a lot of land for immigrants to disperse over.
You're describing a utopia where they can move to Dragass Idaho, population 500, and still be able have total access to all their culture and goods, to their traditional food? No, that's logistically impossible.
In order to achieve what you are talking about, you have to take ONE of every Nationality and force them to settle in every area of the United States...then force every store in those areas to carry the goods, clothes, toys, food, in every store across those 2,600 miles.
It doesn't work like that. The Germans and Poles and Ukrainians, they came to Chicago and New York, so it's Chicago and New York where those cultures still thrive.
You want to get good Mexican food or see a Dia de Muertos shrine, you can do it in California, you can do it in Texas, in Chicago, in New York, New Mexico, because that is where they are settling. You won't find it in Baton Rogue or Savannah because they didn't settle there. And no one is pointing a gun to their head and saying "You have to move to Chicago" when they come to the US.
Conversely, to distribute it the way you are talking, you have to force them to move away from where their friends and family had settled before to effectively distribute the culture across the country.
Even then, Mexican and Irish places are the easiest to find across America because, frankly, they have the highest immigration numbers.
I'm frankly telling you that, to totally emerge America in EVERY culture that has come here, and we are unique in that we have representatives of EVERY nation and EVERY religion and EVERY culture on the globe, you have to do a LOT of forced relocation of the people of those cultures.
It's honestly, a far more peaceful means to just let people come to where they want to live and not force them across the land to appropriately dissimulate the cultures, even then people say American culture is bland, all that merging would be, frankly, boring