If you measure poverty by "how much money someone has," this is obviously true. I'm not convinced giving people money alleviates "intergenerational poverty traps". I'm not against welfare. Giving people money alleviates their suffering, I just don't think it will solve the fundamental problem.
I believe you are completely correct; one often remarked-upon example is lottery winners, who receive a massive lump sum and often end up broke anyway. This is not due to the nature of the lottery cash, but the nature of the people who buy lottery tickets.
I don't know what the parent commenter's life is like so I hesitate to cast too much doubt, but I have found that people who mentally model "the poor" as "essentially like the rich, but without access to resources" have never spent a great deal of time interacting with or relying on poor people (or rich people, for that matter.) [1] In general, there is a far greater poverty of culture and spirit among the "wealthy-country poor" than any middle-class or rich person who hasn't experienced it can imagine. These are people whose great-grandparents were robbed of societal status through offshoring or legal mayhem, and whose subsequent offspring lived in derelict, unprincipled circumstances for decades as the country crumbled around them, and that doesn't even touch the trouble of drugs.
There are many poor people for whom hard cash would transform their lives and the lives of future generations, but by and large these are not the poor people committing the majority of crime and decay visible to the upper classes. For the majority of the "troublesome poor", you could stick them in mansions with bank accounts stocked for six generations, and in two years you'd still have trashed, overgrown real estate and overdraft fees. [2]
[1] = This is specifically restricted to the poor in wealthy nations; poverty in the form of "living poor in the wild country of my ancestors" is different than poverty in the form of "living poor in a wealthy city", which is why dirt-poor immigrants to the US often succeed immediately--their principles and convictions are set up for success, they just needed access to easy money.
[2] = The analogy I most like to use is the bathrooms at my old high school; due to a series of naive clerical decisions, the advanced classes took place on the highest floor of the school, and the basic, remedial classes on the ground floor of the school. The bathrooms on the third floor were mostly clean and working, while the bathrooms on the first floor were perpetually filthy, broken, and covered in graffiti. They were each cleaned at the same rate, but the users of the first floor bathrooms grew up with expectations of trash and graffiti, and thus perpetuated their own dispiriting environment. Money or access to cleaner bathrooms wouldn't have changed their behavior; only a deliberate and manual restructuring of their value systems would, and that is not a hands-off task.
I am astonished to see that you apparently work for a police force. Do you seriously believe that endemic poverty in England can be remediated by regular direct cash payments?
Direct cash payments plus "no broken windows" social policy would be a good start. That's how you can reasonably kickstart widespread social trust and social capital formation.
