The Federal Reserve was
not happy about using QE; they just didn't see an alternative. It was a consolation prize.
The economy was stuck in a rut and needed some kind of kick in the butt. Congress was unwilling to fund another ARRA-like stimulus (the 1st too small), partly because the federal debt was high. Low interest rates were not doing the stimulus job they used to because it appeared the rich decided waiting out the recession and sitting on cash was a better strategy than suddenly investing in business. Near-zero inflation made sitting on cash not feel so bad. Or, invest in Asia: capital-intensive investments no longer paid off in the USA, as manufacturing was shifting to Asia.
The better solution would be to not run up debt so that the Federal Gov't can issue a big stimulus during slumps: classic Keynes, which is basically Grandmother's advice: save up during good times for rainy days.
But there's insufficient incentive for politicians to avoid debt; they are rewarded for short-term improvements in the economy, not long term. We need something akin to a Balanced Budget Amendment that allows Keynesian stimuluses. The law would probably have to kick in gradually so that politicians wouldn't fear a short-term dampening of the economy that could harm their re-election. (Pension problems have a similar short-vs-long-term feedback glitch.)