The fed doesn't pump stocks. It buys bonds and gives good deals on loans. It merely increases liquidity. It doesn't just give money to people.
The money they make isn't "fake" in some sense, like you're making it out to be. It's real utility that they have generated by providing liquidity. Loaning money is not a get rich quick scheme. There is risk involved.
Also, this is getting a little into the weeds philosophically, but injecting large amounts of capital in this way increases the money supply (and by much more than the amount of capital injected). In a sense, this is a tax on everyone who was not a recipient of that capital via a reduction in the purchasing power of their capital. Generally, consumer prices aren't going to go up in this case... but tons of people who had no investments have been looking at this crash as an opportunity to get in the game, and these efforts to prop up the markets with monetary policy in the face of an honest-to-goodness crisis can feel a little gatekeeper-ish.
The market and the Fed have been disagreeing with that rate for what over two years now?