Just because it may not be based on reality does not mean it's not a dream. And of course the dream in the US was probably stronger from 1945 to 1975 when it had the greatest chance of being true. It was then that the middle class was growing rapidly with returning war veterans entering college, starting new jobs and starting new households. The wealth gap between the workers and the upper echelons was not as extreme as today. Also the Horatio Alger, rags to riches narrative was much more potent in the late 19th century in the US and has been deeply ingrained in the popular conception as the article below relates.
This indicates that though Sweden has one of the highest social mobility rates in the world that the top of the income stratum is dominated by people whose parents were rich.
Yes, after the war when the rest of the developed world lay in ruins and America had literally half of the world's wealth it ushered in at least a 20 year golden age for the American middle-class, and the really large wealth gaps started showing again especially after Reagan's economic policies in the 80s (and Thatcher's in England).
Concerning Sweden, then yes, it may be in the better end of social mobility world-wide but it's still not very good compared to the other Nordic countries Denmark, Norway and Finland.
Question: Does that comparison with Scandanavia take into account the growing immigrant community in the father-son earnings?
Sweden has the same percentage of its national population being immigrants as the US (14.3%), Norway being a bit lower (13.8) and Denmark and Finland a lot lower (9 and 5.4, respectively). These numbers also include immigrants from other western countries, of course. (based on the UN report 'Trends in International Migrant Stock: The 2015 Revision'
https://en.wikipedia.org/wiki/List_of_countries_by_immigrant_population).