Why doesn’t the Fed “inject” money into the economy in a bottom-up way sometimes, to prevent imbalance/wealth inequality?

The fed through QE and Low interest rates injects money into the economy. The problem as we have seen is that those “closest” to the spigot(like Wall Street, banks, large corporations) tend to see the most benefits. Those farthest from the spigot(like wage earners) see the least of this money trickle down.

I get that the fed wants to maintain the ability to BOTH put money into and take money out of the economy. Simply handing out checks that cannot be retracted isn’t as fluid.

But… I am curious if the people making these decisions have ever seriously talked about attempting to alter/diversify the way this money is put into the economy. It would seem some method that at least attempts to give the money to the “bottom” of the economy to prevent the wealth inequality, and “near the spigot wealth/power accumulation” would have had to have been considered at some point. Like, even if it 95% buying corporate bonds/treasuries, and 5% stimulus designed to go directly to the bottom rungs, there would likely be value in this, no?

Anyway not trying to be a political post. Just trying to honestly see how central bankers/economists think of this issue, and why more creative ways of injecting the money to counteract the negative effects of constantly putting it in from the top and hoping it trickles down.