Ellen Brown is the only person I know of who writes on these subjects with the level of detail and breadth she does: "Why Is the Fed Paying So Much Interest to Banks?."
If you read between the lines, perhaps you'll get out of Ellen's article that the Fed is paying the banks to still prop them up on the public's dime.
What the Fed did was what the banks couldn't do: be the "bad bank." There were ideas floated that all the losses of all the banks would be purchased by a "bad bank" that would then go belly up on purpose to wipe out the liabilities of the banks. That idea wasn't accepted because it wouldn't have flown with the American people.
What happened instead is that the Fed floated the banks with cash (reserves) and paid interest on that cash to buy the banks infinite time for their junk assets to gain in value again or be otherwise written off in a gradual, nearly unnoticed manner also while the banks used some of the extra cash to continue speculating.
Please notice that, as I've written before, the Fed mandate is not really the "dual mandate" of maximum employment while keeping a check on price inflation. The real mandate is exactly what the Fed did as its highest priority: keep the banks afloat. If the Fed had not done what it did, the US banking industry would have collapsed and the bankers with it. The alternative was nationalizing the industry and then holding on to it or re-privatizing it.
Nationalization is what should have happened.