So you select one country, over a carefully selected period of time, you select one parameter amongst hundreds to explain one other. I'm not very good at US history, but slavery, an almost infinite amount of natural resources comes to mind, more that the tax system. While during this time European countries were still wasting resources in wars, throne successions and a mostly feudal system.

If I give you another country that pushed people out of poverty into middle class with heavy taxes (Germany after the war for example), then I win at telling the taxes are not the primordial criterion?

Or maybe we cut the crap and we look at global data, statistics and economic theory instead of looking at one datapoint and make it an example.

Millionnaires are a very small population, they are statistically irrelevant at the people level. Having a very few millionnaires, all of them self made, doesn't influence the social mobility. Otherwise, a few winners at the lottery in a very poor country (imagine the winners being more numerous than the war profiteers) would be enough to claim that it's a country where there is social mobility. You're just looking at the statistics of an infinitely small population.

edit: and I probably forgot to throw some Chinese railroad workers in there.