This is the reasoning that lets people gentrify.
People wouldn't romanticize NYC the way they do if it wasn't for the cultural enclaves it created. Same for San Fran, Chicago and basically every other big city. It also takes discourages small business as well. When you have a hood that has an identity people are more encouraged to create business that caters to that clientele. No one likes having to drive 45 mins to get real tamales, or have to go two towns over for some Lamb Kafta. I should, by logic, be able to go to the Latin and Arab areas of the city to do that.
Like with Chicago for instance. Gold Coast is nothing like Hyde Park which is nothing like Wicker Park which is nothing like The Loop which is nothing like Calumet....these are all things that people identify with and it tempers how they live.
You don't have that diversity when you try to rip people's identity from them. This isn't like the 60's and 70's when Irish/Italian/Polish people left the cities in droves. We are talking about the people who CAN'T AFFORD to leave. I'm not against making an area better...but you can't say it doesnt matter. Because it does.
The fact that you can say there is no such thing as a neighborhood with an identity lets me know you aren't ready for what you propose.