One can argue that high levels of income inequality aren’t much of a problem when social mobility is easy (social mobility being the degree at which people cross into higher or lower income levels than the ones they were born into). Inequality is then the result of skills and effort, the absence of skills and effort, or lifestyle choices. In other words, given easy mobility, inequality is what people deserve or want. If there are few or no obstacles to mobility, people basically choose their position in society: they choose to develop their skills and invest effort, or they don’t.
However, this whitewashing of inequality doesn’t work because the more unequal a society, the less social mobility there is (source).
What is the mechanism here? In part, high levels of income inequality make social mobility more difficult: when income inequality is relatively high, people at the wrong end of inequality can offer comparatively less opportunities to their children than the people at the right end – less quality schooling, less quality healthcare etc. The children of wealthy parents have relatively more advantages compared to poor children then they would have in a less unequal society, and they are therefore more likely to end up in a high income group as adults. I assume that social mobility is a good thing and that people’s income should not be determined by the income of their parents.
So instead of saying that inequality is not a problem because there is mobility, we should instead say that mobility is a problem because there is inequality.