I'm left unsure what your point is.
Saying that you have to look at social mobility as a relative thing is certainly false, because we have an optimal yardstick: perfect fairness. If measured against that goal we don't do very well.
Then you go into what the relative numbers are, and it turns out we don't do very well there either, being behind China, Hungary, South Africa and perhaps a dozen others on your preferred yardstick.
You then note that there are at least one or two more cases of this happening (which I believe), and that it requires capitalism with a social safety net to do so. In current application the first part is right, but isn't broadly correct, and the second part just isn't true.
Regarding the first part: for such a huge change in life circumstances to happen you have to have both the extreme poverty and extreme wealth. Capitalism is very good at generating those huge disparities, and is by far the most common system with that characteristic today, but monarchies like Saudi Arabia also experience it (extreme individual changes in SES in Saudi Arabia are most downward, however). The presence of a social safety net doesn't seem to play much of a role in these extreme cases, and certainly didn't in this case. Examples of self-made millionaires going back to early colonial history abound, and certainly there was no strong safety net in place. Given the relative infrequency of such events, I would be skeptical of any attempt to compare between two historical periods or societies based on relative count between those societies or periods as well.
After all that the only thing I can think you were trying to say is that the US is doing a-ok, which just isn't supported by the points you made.