I read about another study relatively recently (maybe it was HN? Not sure.) that talked about some of the fundamental flaws when looking at these types of economic mobility studies (i.e. change of moving from bottom quintile to top quintile, etc.) because they usually only look at income and ignore
social class.
That is, suppose Bob is a rich banker. His kid Frank goes to private school and on to an Ivy League college, but seeing how distant and money-focused his dad was growing up, Frank decides to become a writer. Frank is certainly not poor, but he definitely lives on a very modest income and that is what his son John experiences growing up. John, not wanting to have to be in as modest circumstances as his Dad, decides to follow in his grandfather's footsteps and become a banker. His grandfather is even able to introduce him to some colleagues and get him some interviews at top investment banks.
Point being, if you just look at income, it will look like a dynamic economy with lots of economic mobility, with each generation moving from the top to the bottom of the economic latter, and vice versa. In reality, though, nothing really changed at all about their social class and the opportunities that were open to them. Unlike most people in the bottom half of the economic spectrum, Frank was basically there by choice.
Again, you may think this is an extreme example, but in my experience I have seen some version of that multiple times.