One of the exceptions in the US seems to be around the White House. For a while, when Hillary Clinton was running for President in 2008, it was possible that the US would have had a member of the Bush or Clinton families as either VP or President every year from 1981 thorough to 2017. Such political families are not unique to the US, of course, and the UK has a fair few, too: https://en.wikipedia.org/wiki/Political_family
With that, Bill Clinton has very humble ancestry, as does Hillary; both trace back to traveling salesmen, small business owners, coal miners, such kind of folks.
Parental families of, say, Nigel Farage or Margaret Thatcher were somehow more sophisticated, even though not tracing back to some nobility.
Not that coming from a well-off family is bad; I just would like to emphasize that the "American dream" of coming to high social positions based in merit, not lineage, worked for Clintons.