Eugine_Nier's comment has the suppressed premise that status usually results from character traits (alone, or primarily). NancyLebovitz's response contradicts this suppressed premise.

If you get rich by being exceptionally virtuous, then redistributing the wealth will make it less obvious who is virtuous.

But if you get rich by having a rich dad, then redistributing the wealth will merely make it less obvious who had a rich dad.