They're almost intent on keeping the funds within the financial sector. Why would they 'spread it out'?
But the point is that it can't do any good in the financial sector ('pushing on a string'). If it were sent outside that sector it would be spent, thus actually having a growth effect.
Apparently no one at the Fed has studied the great Depression or Japan.
Given that the Japanese invented QE and given Bernanke's reserach background...lol.
They don't want to redistribute wealth, only increase liquidity (that is oversimplifying a little bit of course)