As the Volokh article about the mobility of the poor (and internally linked article) points out, there are types of benefits - Section 8 housing comes to mind - that can keep you locked into collapsing Detroit when there might be jobs in another area. Those people don't have full time jobs anyway, you tell me, so it doesn't really matter? Yeah but their kids are going to need jobs, and there are jobs in North Dakota or San Antonio, which they can't access. When they turn 18 they can strike out on their own and hope for the best, but that is another level of risk that children in nicer places don't have to endure.
As the only proffered solution was the centralisation of welfare benefits - oh gee, what could ever go wrong with that? - I don't have anything quick to suggest. But while solving this problem would only solve a portion of poverty issues, it is a portion that could be lasting. People get jobs, stumble along a little better just like the rest of us, starting a virtuous cycle for their own children - there's just that much less to fix.