This concentration of people required more services both because of the sheer higher concentration of people and because of the lack of private money to backstop gaps. At the same time, those areas received less services/investment precisely because the people who lived there were not powerful. This gap of services lead to increased crime due to factors such as lack of opportunity, increased drug abuse due to hopelessness, worse education options, etc.
The gap widened and got worse until it became untenable to maintain (and in some cases the land became too valuable) and political power was used to disperse the public housing population.
Suppose inequality were lower and those rich people simply didn't exist. They would still be unable to provide resources, and the low level of services you describe would still exist. Wouldn't the crime/drug use/etc still happen?
That is not what I said. What I said was that the powerful moved the poor, into higher density, more resource intensive areas and then neglected to provide adequate services.
If the inequality were lower and those rich people (and really I prefer powerful in this case, but they are largely the same group so I suppose it is fine) did not exist, the concentrated population would be diffused across more areas, making it less tenable to actively neglect them and making the problem less severe in the first place.
That said, I believe crime/drug use/etc are not avoidable, so its not a question of whether those things would occur but a question of the rate.
At least here in India, with significantly less inequality than the US, we still have lots of concentrated poverty. It's almost as if residential separation is the result of market forces and individual choices (c.f. the Schelling model).