Lane Kenworthy, a leftist confiscatorian, has published an article with charts showing that the government action which most reduces inequality is not taxation itself, but transfers.
In other words: the aspect of government which achieves the inequality-reducing effects that leftists desire is not that it punishes the rich; it is the transfer of money to those with "less". It does not matter much whether the money was originally confiscated with a progressive income tax or a flat sales tax or whichever method.
Consequently, Lane goes on to propose that the U.S. should consider a national sales tax in addition to the existing income tax system, so as to alleviate the suffering of the masses. Who undoubtedly suffer much. [/sarcasm]
The problem with reducing inequality is that equality is inherently unfair. Some people want to strive to have more, others aren't willing. Why should those who are willing to strive be denied their rewards?
On the other hand, people suffering and not being given opportunities for no good reason isn't fair either. But to help alleviate such pointless and unnecessary suffering, it is not necessary to reduce inequality. In fact, I believe that policies aimed specifically to reduce inequality actually increase suffering.
Policies intended to alleviate pointless and unnecessary suffering should aim to alleviate pointless and unnecessary suffering. Not reduce inequality. Inequality is not suffering. Unless, perhaps, you count feelings of envy as reasonable grounds to complain.