I think there's a distinction between forced poverty and chosen poverty. Are the poor people you're talking about actively trying to become wealthier? If not, then poverty isn't the real problem.
A group of Cherokee Indians in North Carolina got some money from opening a casino. They decided to share profits, giving $6000 a year to each person in 2001 for instance. It's more or less a basic guaranteed income. So what happened to these people who'd lived in poverty before and now got a bit more money?
Children who were moved out of poverty saw behavioral problems declined 40%, crime declined, and high school graduation rates increased. Like magic! See [1] for more. Main takeaway -- money increased parenting quality; parenting is key to success.
Money can solve a lot of problems. Do you know how regular people try to actively become wealthier? They work more hours a week at minimum-wage jobs (ok -- add a second 20-hr/week part time job to your 40 hrs and you make less than 550 extra a month after taxes, and you are working 60 hrs/week so can't care for your own children that well). Or they become real-estate agents. That's a waste of time. If actively becoming wealthier were so easy these scrappy hard-working people would have done it.
I disagree with poverty being the root of the issue. It's one of them, but not the primary one. There are many examples a society was desperately poor but they escaped it with education. Look at some Asian countries. Good example is S Korea. They were desperately poor just barely 1-2 generations ago. The cards were really stacked against the country (no natural resource, infra wiped out by vicious 3 year war, uneducated population, requirement for maintaining large army etc) 6 decades ago, and it was pretty much just improving education that got them out of the hole.
How do you fix poverty? By fixing the education.
Oh wait, hang on...