In almost all discussions of social mobility, the measure is intergenerational mobility (do you end up in the same socioeconomic class as your parents), not if you made more later in your career than when you started. Almost everyone makes more later in their career than when they started, that's not a sign of upward social mobility (at least not on an intergenerational level).
For some reason, you cherry picked the one study that looked at all incomes in one of the most prosperous periods in the US. https://en.wikipedia.org/wiki/Socio-economic_mobility_in_the... does a good job of summarizing a number of studies that show that the US ranks as one of the least socially mobile countries in the world.
No one is arguing that people make the same amount their entire career. That's not what social mobility is. The fact is, the US has one of the lowest levels of intergenerational social mobility, and that exceptions to the rule are held up as evidence of The American Dream in action. It's not impossible to end up better off than your parents (in relative inflation adjusted terms), but that's the exception, and it's usually due much more to luck than hard work. Millions of americans work hard and end up exactly where their parents were.