This remark of yours is truly an ideological minefield! I completely agree that the debate on income inequality and the resulting sorting of people is irreleva

This remark of yours is truly an ideological minefield! I completely agree that the debate on income inequality and the resulting sorting of people is irrelevant. Income inequality itself is irrelevant, it's just an ideological misdirection. But, since you proclaim to be libertarian, I suppose you wouldn't agree with me on why it's irrelevant: it's being pushed to actually preserve overall capitalist relations. Sacrificing low taxes of a billionaire or two is a small price to pay to help the ruling class keep ruling. This is practically the central theme of Keynesian economics, and thus of a great deal of 20th century. The strategy is still extremely effective, and so in this election cycle we had good old Bernie Sanders act as an acceptable vent for social and economic discontent of working people by ranting about “the billionaire class”. To anyone not horribly politically illiterate (sadly American culture is generally grotesquely politically illiterate) it was painfully clear from the moment he entered the primaries how his “revolution” will end. So income inequality discourse not only does not help alleviate the problem, it maintains it. Democrat-style liberalism is so effective because it's an ideological Escher drawing. To even start to explain why it's wrong (or even better: why it's not even wrong!) and even in many cases harmful, you have to rewind the arguments aaaall the way to first principles (let's ignore the likely case that then you end up with the problem of getting people to universally agree on a coherent set of first principles) while constantly being under the threat of being, 1930s Pravda style, denounced as pro bigger evil. As a friend of mine recently semi-jokingly said: “There are no bad guys, just a liberal hell in which all is mixed, a hell in which evil people do good things and good people live in a fantasy.” As for mobility, there really isn't any significant mobility, this is empirical. Unless you count moving from lower middle to upper middle class (I'm not sure even that is a significant case, I just assume it is, but even then it's likely plastered with all kinds of demographic qualifiers). But still, income inequality in and of itself is not a cause of this, it's one of the symptoms, and not a particularly onerous one.