I don't think much good comes of artificial segregation based on income level or other factors associated with it.
In the olden days--in this country I mean really really a long time ago--but you still see it in other parts of the world either from legacy or they still do it--rich and poor lived fairly close together. Often rubbing shoulders--the manor houses contained live-in staff who were penniless.
In some parts of the world you still see mansions looming over hovels. In some parts of Europe you can see working-class housing within very easy walking distance to mansions. They were separated, but by no more distance than necessary to fit enough of each social class to make it a neighborhood. Indeed, servants HAD to live within easy walking distance of their employers! Unless they were live-in, but that was probably less common in the cities aside from maybe a few key staff needed 24/7 (personal helpers for the elderly, nursemaids, that sort of thing). 10% of the population of Jolly Old England were domestics!
Why the difference? I would guess more than anything else that in the old days, for better or worse, crime was taken more seriously IF THE VICTIM WERE RICH. I know that murder rates in Jolly Old (18th century) England were dramatically worse than in modern-day New York City (contrary to common belief that high crime rates are a modern phenomenon. Actually, they go up and down in long cycles). Then, as now, the police only bothered to investigate a small fraction of crimes--but they tended to favor and defend specifically the rich more blatantly than they do even now.
I doubt they were any safer. Probably not! But it was probably more of a psychological feeling. They were more used to the idea of living closer to the poor than their successors are.
In his book "The road ahead", Bill Gates envisioned an extreme of wealth-segregation, with the wealthy living in deep-rural resort-type communities, the idea being that technology would make it possible. I doubt the trend will go to that extreme, but such has been the trend.