Economic models of wealth inequality tell us not to worry about it. We should not worry about it because it cannot happen. The theory assumes that the distribution of wealth is stationary. According to the theory, individuals move up and down the distribution, but the distribution itself is stationary. This, in turn, assumes that individual mobility is a constant. That is the end of the subject because theory trumps empirical reality.
Thomas Piketty has made an effort to explain why the distribution of wealth is not stationary. That has inspired a number of conservative economists to provide a rationale for the assumption of individual mobility within a constant distribution. It is almost unpatriotic to question that assumption because the idea of "American Exceptionalism" depends upon it. Everyone knows someone who rose from rags to riches, and we even know someone who moved from riches to rags. Therefore, the mobility assumption rests on solid grounds.
It turns out that rising wealth inequality is better explained by the high correlation between parental wealth and the wealth of their children. The concentration of wealth tends to increase over time, and so does individual mobility within the distribution. None of the efforts to defend the assumption of individual mobility, described in this article, are supported by facts. If one is rich or poor it is best explained by the wealth of one's parents. The distribution of wealth is not stationary and we should not accept economic theories which assume otherwise. If we care about rising wealth inequality we should ignore those who defend the assumption that the distribution is stationary. Government policies can alter the distribution if it chooses to do so.