QE was the central bank buying bonds, not selling.
They bought bank assets and "paid" by increasing that banks reserves on deposit in the Fed Bank. One blogger said it was like when you transfer money from your savings to checking, you don't gain any money, you just have more available to spend, or in the banks case, more to loan.
The other thing that happened was the Fed started paying interest on those excess reserves. The upshot is, most of the QE didn't go anywhere because a) the market for CDOs and MBSs went kaput so the banks once again had to actually pay attention to who they were lending to; and b) they probably peed their little banker pants when the whole thing went tits up and were afraid they would actually be regulated like they should have been all along.

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Look at it like this; there is "private money", the 90% that dave talks about, that is IOUs we get from the bank when our paycheck clears. Then there is government money, cash and bank reserves. The banking system is a for-profit, market-based money system. The idea is loans get made based on market conditions and on the Feds interest rate and regulatory policies — not on the whim and ideology and convenience of politicians.
Turns out, the great recession was brought about in large part by the whims and ideology of Allen Greenspan who held rates very low after 9/11 and who thought that the market
needed no regulation; that bankers would police themselves [ETA: Clintonistas and BushCo of course felt exactly the same.] Unfortunately, the bankers found a way to disguise and pass off risk to people obviously not equipped to deal with it. Most of them got away with it.
$this->bbcode_second_pass_quote('', 'T')he maestro admitted ... that he had "made a mistake in presuming" that financial firms could regulate themselves.
Recurring bank crises stemming from lack of regulation don't mean the system should be scrapped and handed over to politicians and bureaucrats, it just means it needs to be better regulated. A completely political, government money system at the beck and call of politicians whose job it is to give their constituents ever more stuff —including ever lower taxes, is definitely not an answer.
Although I don't see how politicians could do much worse than the current bubble...