It is a maths problem, not one of economic theory, and a well-understood limitation of "social mobility" as a measure in this context. Social mobility between two countries is only meaningfully comparable if their income distributions also have a similar degree of compression since it is a rank statistic. The large differences in wage compression between e.g. Scandinavia and the US are well documented, such as this[0] recent NBER paper, and not controversial.
Increasing rank is much easier than increasing income on a compressed distribution. Being able to easily increase income is much more important than being able to easily increasing rank if you are optimizing for economic opportunity.
Yeah, median income in the UK is about at the level of Mississippi, as is much of Western Europe (Western, not Eastern!). The US is just ridiculously wealthy, and our income inequality is largely a matter of the absurd heights reached at the top, with wide distributions. OTOH, wealth disparity (or even just the perception of wealth disparity) can be politically destabilizing and lead to some pathological social issues. Greater relative social mobility and greater (perceived?) wealth equality seems to result in a better sense of fairness, a sense of fairness is key to social cohesion and trust, and social trust is key to producing wealth. Though, social trust is necessary but hardly sufficient. Likewise, perceived mobility and equality seems necessary but not sufficient for healthy political and civic culture.
[1] https://www.oecd.org/content/dam/oecd/en/publications/report...