I think the United States is divided to the point where Democrats should live in one area and Republicans in the other...
That's pretty much the way it is. Democrats live on the east and west coasts and in the big cities, and Republicans live in all the rest of the country.
That would be an interesting social experiment. Take a city, split in half dems one side rep the other. See which side fairs better both economically and socially.
No. It's divided, and that's a problem, but furthering divisions will not help.