Well, the main issue here is social mobility - most importantly escaping poverty and becoming middle class (and also not falling back into poverty), not just becoming wealthy. As has been stated elsewhere in these comments, there is enormous selection bias regarding those that choose to immigrate to the US from other developed countries in an effort to "become wealthy."

With this in mind, generally speaking the US does not do particularly well on social mobility in relation to most other developed country, this includes the Scandinavian countries, the other anglophone countries, and western/central European countries... And, honestly, it really should surprise no one that social programs (including things like high quality public/affordable education and universal healthcare) improve social mobility for the poorer half of society.