This is, in fact, the opposite of true. As noted below, pretty much every wave of American immigrants until recently (Irish, Germans, Italians, Southeast Asians) came here desperately poor and eventually attained economic parity with the groups that were already here. Indeed, that process continues with Hispanic immigrants: https://academic.oup.com/qje/article/135/2/711/5687353 ("Hispanic Americans have rates of intergenerational mobility more similar to whites than blacks, leading the Hispanic-white income gap to shrink across generations.")
In the U.S., structural poverty affecting a discrete minority affects Black and Indigenous people, and certain white sub-groups such as Appalachians and Cajuns. It's not a good default model for thinking about income mobility in general.
> there is little evidence to suggest that this corrects itself after a few generations
On the contrary. The vast bulk of modern American citizens emigrated to America as poor, even destitute, people. Look what happened to their descendants.
There are a massive number of examples of this being untrue in America. Jewish Americans, Cubans, Irish, Asian Americans, Poles - all these groups started out poor, and regarded as something other than and lesser to "white" people, and now have at least the same incomes and often more.
The people you are likely referring to for the chattel excuse history also under perform in country after country where such things were never allowed. Diversity is difference, and difference will lead to persistent disparity.
I would have guessed it would be incarceration. Do you have some numbers to support your belief? Wealthy parents likely were not incarcerated, so there may be overlap.
As for numbers, here's some: https://www.businessinsider.com/parents-determine-child-succ...
Thats a perfect example of unequal opportunity. As much as we try to make excuses around it, the single biggest predictor of someone's lifetime income is their parents income. The fact of the matter is being rich provides opportunities and advantages being middle class doesn't and definitely not being poor, and there is little evidence to suggest that this corrects itself after a few generations. The fact is historically poor populations tend to stay that way, with those who escape being outliers.