Relative poverty will always exist as long as income inequality exist. For the same reason that as long as people are given “As”, there were be other people who will get “Fs”.
Absolute poverty, however, isn’t an intractable problem. All over the world, even in undeveloped places, the standard of living is going up. In the US, it was normal for poor kids to walk to school barefoot and go the entire day without eating. While I live in a town populated by poor kids, I don’t see them walking around barefoot or walking around with pellagra, and I’m quite happy about this. What this tells me is that there is no rule that says poverty has to be any set thing. It’s all relative.
We could design a society that guarantees basic housing, ample nutrition, and medical care for every single person. We would still have poverty. The people who would be labeled"poor" would still feel stigmatized and demoralized. But their situation and that of their children would be leagues better over what we have had historically. If you don’t have to worry about housing or getting the babies fed, then you can concentrate on getting a job. Then you can concentrate on getting a better job. And your children will be more likely to do better than you did.
Seems to me concluding the problem is intractable guarantees that’s what it will be. But it’s not. Completely alleviating poverty is a pipe dream. But making poverty more dignified isn’t.