Poverty has not a thing to do with crime. Crime is the end result of disrespect fostered by jealousy and envy. There has been endless lack of respect taught at many levels, that there is some sort of unwritten right to take from others if you lack possession of some sort of internal compass. This trait is unrelated to economic status.
Nowhere in the Ten Commandmants is there any admonition, "Thou shalt not be rich." There are various ways in which you may not enrich yourself, such as stealing, or coveting your neighbor's wealth, or turning to the worship of Mammon, and certainly there is a strong prohibition against killing, for the purposes of taking the goods that once belonged to a person now dead.
All that aside, poverty is a state of mind, not an economic condition. Even the poorest among us has, from time to time, come onto a windfall. This is a grace, bestowed upon the randomly selected, that for even an instant, gives the illusion that wealth may come to anyone. One may do one of two things with a windfall, either splurge and disperse it with all possible haste (some haste is more possible than others), or use the new-found capital to build and take on a calculated risk, in the hopes of greater return in the future.
Consider the plight of a winner of a multi-million dollar lottery. Unprepared for the burdens of sudden wealth, the tendency is to vastly overestimate the limits of that fortune, and spend it quickly. Very corrosive to the character, the victim of this endowment is left bereft and often in a degree of debt unimaginable before the influx of cash. That is the essense of poverty, the inability or unwillingness to manage money in any sense.
I generally agree with your post as regards to the US, and to a lesser extent with regard to other developed countries.
However, we should recognize that in much of the world, there are indeed far fewer opportunities available.
As has been pointed out, the level of work and striving that will keep you alive in China or Vietnam will make you rich in America.
Individual effort is critical, but it is not the only factor influencing whether a given person will be poor.