Social mobility is a measure of relative rank change. In countries with compressed wage ranges, such as those you mention, “social mobility” is an artifact of the mathematics, it doesn’t mean you are meaningfully wealthier than the average person. You can double your household income in the US to above average and still not be “socially mobile”. Social mobility is not a meaningful measure for continent-sized economically diverse countries.
A person can go from the trailer park to being upper middle class in a place like Mississippi and it doesn’t count as socially mobile because you are being ranked against the household income of someone in Seattle, 3,000 km away. As far as the person in Mississippi is concerned, they are living the dream.
The opportunity to improve your standard of living in e.g. Europe pales in comparison to the opportunity to do so in the US. It won’t be classified as “socially mobile” in the US as an artifact of how the math works, but no one in the US cares.