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 cannot reduce inequality on its own; far from it. This requires a concerted effort by the government, broadly speaking, to support a variety of efforts. These include things like raising the federal minimum wage, eliminating unfair restrictions on union organizing, increased fiscal spending on needed infrastructure with a condition that these jobs will be decent paying jobs. Of course, this is just the tip of the iceberg, and far from the question of the role of the Federal Reserve.

Raising interest rates might lead to some initial reductions in wealth by lowering asset prices, but it could also take a bite out of your paycheck and dampen your prospects of finding a job. It's a bit of damned if you do and damned if you don't.

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.

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.

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.

Critics, often for good reason, are concerned that the Fed is wielding its vast powers in the interests of the banks and not in the interests of the people. After the financial crisis, Americans have perceived that the banks have been bailed out, but a significant proportion of the population is still in serious economic trouble.