Earlier quoted context omitted.
As long as the police still do their jobs, why does the existence of such an underclass worry you?
I can't think of any U.S. law enforcement agencies that have ever asserted (either as a primary or secondary mission) to take care of or otherwise manage the impoverished underclass. Can you cite any examples that you know of?
The only downside of creating an underclass is when they commit crimes; but managing this downside is part of the police's job.
(n.b. income inequality isn't illegal; theft and murder, are.)