Is there any statistic to show what percentage of today's top 1% earners where born to a bottom 50% family from the previous generation, and viceversa? If less than what you would expect from two non-correlated random variables, this suggest where you start in life has an effect of how far you can go. This does not invalidate your hypothesis, but may suggest that upwards mobility takes more than one generation to lift people from poverty to wealth.
Further more, we can do the same analysis to figure out how many people from bottom 50% families grow to reach 75% percentile or above. I do not know what it would be, but if much lower than expected, that would suggest that upwards mobility is quite limited, invalidating your hypothesis.
