We want people to live in diverse neighborhoods because people who communicate and interact with other races on a daily basis are far less likely to hold bigoted or prejudice views against those races.
The implication is that people who don't live in diverse neighborhoods are racist.
I didn't choose my neighbors because of their race. I chose my neighborhood because it is near my family and my work and because I just like the town. It's not particularly diverse, but I don't know of anyone who is racist either. I don't think any of my neighbors would care what the skin color was of a new neighbor.
People who grow up in exclusively (or vast majority) white neighborhoods are more likely to form opinions about other races based on what they see in movies or on TV.
Why do you mention white neighborhoods specifically? Is it not possible for people in black neighborhoods or Asian neighborhoods to do the same thing? (Although I am not saying they do.)
By your logic homogenous neighborhoods are unhealthy because they breed bigots and racists. Or are just homogenous white neighborhoods unhealthy?