I was being rhetorical, but your comments here are a fine example of one of the reasons why they don't: lack of a sense of ownership.
Let's set aside for a moment all of the other factors into why poor neighborhoods tend to be run-down and crime-ridden -- lack of resources, hunger, hopelessness, crime, drugs -- and imagine a neighborhood filled with perfectly rational poor people.
We'll take Bob as an example. Bob rents a house for slightly less than he can afford from a landlord that, for whatever reason, is not interested in fixing the place up and demanding a higher rent. Maybe it's because the landlord also doesn't have the funds; maybe it's because all the other places in the neighborhood are run down too, so the landlord could never realize as much value from improvements.
In Bob's neighborhood, none of the houses are freshly painted, because it's in nobody's best personal interest to do it, because they don't own the places. None of the yards are weeded or landscaped, the plumbing leaks, and the wiring is hazardous. Bob commits as little of his own resources to his house, because it doesn't belong to him.
Eventually, the neighborhood becomes the victim of its own disrepair, and is no longer worth investing any money in at all. Bob, being perfectly rational, simply moves into a similar situation at another neighborhood.
A wealthy investor shows up, purchases the homes for the rather low amounts that they command, from landlords happy to be rid of them and getting anything at all for them, and kicks out the tenants who simply move into other neighborhoods and repeat the pattern. The investor razes the miserable houses to the ground, which is probably the right thing to do at that point, and builds whatever their market research firm tells them is most valuable there -- a shopping center, parking, condominiums.
This, indeed, is a cycle that is being played out every day all over the U.S.; I've personally seen it in more places than I could easily recall.
But, I question that system. I think, if Bob weren't a rational actor, if instead he moved into a community and decided to behave as though it belonged to him as much as anyone else there, and subsequently started fixing little things here and there -- and then his neighbors did the same, because they didn't want to suddenly have the worst place on the block, and so on -- then, perhaps, poor people could discover that they can afford to live in nice neighborhoods after all.
G'night.