Here's the interesting thing: the fact that QE and lowering interest rates almost to zero has worsened inequality, does not mean that raising interest rates will help reduce inequality.

People in America get really angry at the Federal Reserve and at the "money system" in general during economic crises. The Fed draws hostility because of its power, its insulation from democratic accountability, its lack of transparency, and because of its historical and structural connections to finance.

Bankers themselves govern the Fed to some extent, and then there's the classic revolving door where Fed officials come from and then go back to the financial sector. Fed officials tend to believe that the institution should have a large measure of independence from democratic control, even though in law it is under the ostensible control of Congress.

Many of those on the right distrust the Fed and want to eliminate its power in the belief that the private economy, including the private banks, will be much more efficient, productive and even democratic if they are left to themselves: in other words, the criticism of the Fed really reflects a desire to cripple the government in the service of increasing the power and authority of the market.

The right wants to destroy the power of the Fed to increase the power of finance; and the progressives want to reorient the Fed so that it will stop protecting the interests of finance and protect the interests of the broader population instead.

The Fed has a lot of power in the economy because it has a big impact on the supply and cost of credit, that is, interest rates. It also plays a key role in supervising banks and historically has seemed to take it easy on the banks when it shouldn't have, such as in the lead up to the financial crisis.

QE and other aspects of Fed policy increased inequality pretty significantly. This is reinforced if you take into account all the other non-standard measures the Fed used to bail out the banks early on in the [2008] crisis.