In addition to what nbome said, I think a part of the reason is that if you use the new money first, the prices have not adjusted to it. Those that use the money last are hurt the most and those that use it first benefit most.
To help illustrate this, imagine five classes of people, ranked by their order in getting their hands on new money: A, B, C, D, E.
A gets the money first and buys things from B. B notices a lower demand for cash in A and adjusts prices accordingly. B buys things from C and C notices B’s lower demand for cash and adjusts prices accordingly. It goes on like that, down until the last recipients. Obviously society is not divided up into A B C D E but you get the idea. This is the essential non-neutrality of money. It’s behavior can only be informed by the purchases it facilitated, subject to the changes of market data.
Basically, JPM gets to buy stocks at 36$/share or gold at 1600$/oz and you get to buy it at 39$/share or 1650$/oz.
EDIT: This is in regards to Fed asset purchasing, not their discount window: the Fed buys bonds from banks. The effect of this may be to lower interest rates from increased money in the loan market, but it’s also nice solid business for the banks. After all, “a little bit of inflation is good for the economy”.
EDIT: Bear with me here, I but I think another plausible explanation for low interest rates is actually a bust as a means to dirty cheap stocks. I think that many in the upper-echelon of finance realize that, in a boom, the options are acceleration of credit expansion or bust. With this knowledge it is possible to become really wealthy: store wealth in more solid areas (like metals), maybe ride the boom and sell off a bit, wait for the crash, and buy the heck out of the dip and wait for the glorious QE action to roll in.
There is a myth, which I cannot verify but find plausible, that a certain english finance family made their fortune doing just this in the Napoleonic War (and in other catastrophic periods for that matter).