Most Americans want to live in integrated neighborhoods -- but different groups have different standards of what the right balance is. This leaves most people not getting what they want.
Reynolds Farley and his students did studies on black and white preferences in the 1990s. Most black and white Americans would like to live in an integrated neighborhood. The most common African-American preference would be for the neighborhood to be 50% black. Most white Americans would prefer their neighborhood to be no more than about 15% black. You can see the problem -- neighborhoods passing the 15% black threshold are more attractive to African Americans, but less attractive to whites; such neighborhoods tend not to stabilize at 50% black, but keep going to nearly all black.
Since the Farley studies were published, the nation has gotten more diverse, so much so that most researchers would not limit their studies to just black/white integration. This is a good development. The more people see that the options are not just black and white, the harder it is to think of a single tipping point that would make a neighborhood head to all one group or another.
What is striking to me about the Farley preference numbers is that most white Americans would like to live in neighborhoods that are as black as America as a whole is. African Americans make up at most 12% of the U.S. population (despite the widespread belief that the proportion is much higher). This is also about the same size as that mish-mosh category, "Hispanic."
Here would be a good study. Suppose you offered people the hypothetical option of living in a neighborhood that was:
5% All others
I think most Americans would go for it.
That is, I think most Americans would like to live in a neighborhood that looked like America.