> 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.
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.