It's a snapshot of a set of dynamic systems. The systems result in the current snapshot.
It's like taking a still-frame picture of a pool table. You can't tell what balls were moving in what direction or how fast they were moving. Perhaps they're all still? Perhaps just one or two are in motion. Are any spinning? Yet the positions are one part of the necessary description before you can make any predictions. You need to know about spin, you need to know about momentum. The snapshot doesn't get you very much.
You can't change the snapshot. You can only change the systems. We know that overall, the rate of change between wealthy groups and poor groups has been increasing: white, black, brown, each community is splitting and has been for 20 years. Race matters, but it's a declining part of the system. It's hard without the statistics to separate out the two components.
The systems are different for different race/SES groups. Latinos come out worse in the bottom analysis in the OP. On the other hand, they're also the most dynamic system. The current snapshot is due to a lot of recent immigration of poor, low education adults and young adults, which naturally results in disadvantages. Their kids have fewer, and if you break the non-monolithic Latino cohort into subcohorts you see this. Nobody likes doing this breakdown because it weakens progressive arguments, makes it clear that many social problems for many people are short-term and circumstance-contingent (and not something we can fix today). It also creates a new set of embarrassing arguments--the Latino population has bifurcated and where a Latino family lives seems to be helping to determine it's social trajectory. You immigrate and land in a mostly low-class neighborhood where the cultural indicators are one of the disadvantaging factors and there are no jobs locally and you're going to track more like that community. You land in a more mixed neighborhood or one that is mostly Latino and you track socially upward.
There's a low chance of going from the bottom to the top income quintile in the US. But there's a good chance for members of most low SES groups to go from the bottom to the other three quintiles; we don't like saying this because it's all about getting to the top, not just doing well or doing better. However, if you look at certain subcohorts the numbers fall; that's what this analysis tries to get at and fails to do adequately because it's ultimately about advocacy first and not description. The social mobility is good because it means that most of those with 4, 3, and 2 disadvantages will lose one in the next generation (while others have to gain one, at least on paper--if we all had an additional $100k in income beginning in 2017 there'd still be a lowest quintile). However, if we acknowledge that most of the people will naturally wind up in different quintiles it gives us advocates and progressives a weaker argument and makes us less important. Then there's the embarrassment felt because the members of those suffering from generational poverty tend to have a number of common factors that are simply not allowed to matter but which matter greatly. As other members of self-defined groups advance over the decades, those particular subcommunities don't.
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