The lack of social mobility is well documented, and it's a travesty that's affecting large parts of the developed world still (and shamefully, the UK pretty much leads on it):
https://www.minneapolisfed.org/institute/working-papers/17-2...
https://www.suttontrust.com/newsarchive/disturbing-finding-l...
https://assets.publishing.service.gov.uk/government/uploads/...
https://www.theguardian.com/society/2018/jun/15/social-mobil...
Unfortunately I'm not as well versed in reliable US sources, but there are references through here that the US doesn't exactly beat us hands down on social mobility either.
I do implore everyone to read more on this topic, there's a lot on HN about "meritocracy" and "well, just work harder", but that's just simply not the world we live in. It's a shit-show out there, and people's ability to break through the "class-ceiling" is being stunted, not improved.
I think a roughly accurate statement is that over half of Americans end up within one income quintile of their parents.
That doesn't seem like much mobility to me and many European countries apparently rank better. The American Dream might be mostly marketing at this point.