I've noticed that libs tend to focus on economic metrics like "intergenerational economic mobility" instead of class when they discuss economic inequality. Basically instead of getting rid of classes altogether they want ''increased mobility between classes,'' or, more accurately, since they don't really focus on the relationship to the means of production at all, and instead they just focus on "income brackets" regardless of whether you own capital/land/means of production or not, they actually want ''increased mobility between income brackets.''
So they want it to be easier for a high earner to become low again, and a low earner to become high again. They view ''increased volatility'' in an individual's earnings over one lifetime as an ''indicator of a healthy society.'' because when so-called "economic mobility" is too low, class status becomes set in stone from birth to death, like slavery or serfdom, and it is harder to sell the prole on the "rags to riches" story that is used to justify capitalism as "free" and "full of opportunities for those who work hard." But how is this increased volatility of rich becoming poor and poor becoming rich an indicator of health? Doesn't that make society way more unpredictable? You wouldn't want that kind of volatility in the stock market, so why would you want it for "economic mobility?" Even from a capitalist perspective, wouldn't it make more sense to want either consistent ''growth of wealth'' across ''all income brackets'', i.e. poverty reduction, i.e. "rising tide lifts all boats"? This is what China aims for, for example.
The economic mobility thing is just meritocracy BS. They imagine that smart poor people will get rich, dumb rich kids will lose their money, and eventually everyone will settle into the class that they "deserve" to be in. It's why libs are so two-faced when trying to help disadvantaged groups - only socialists explicitly reject the logic that social and economic classes should exist at all, libs and conservatives both believe that their own group should be on top.