Earlier quoted context omitted.
I could be wrong but I don't think buying US treasuries would directly increase wealth inequality, since the money is being used to fund the US government. If the Fed bought other more private assets off the market (which I believe it does) then yes it could increase wealth inequality
Possibly, I may be confused between simply buying treasuries, and quantitative easing. Still learning!
Buying treasuries = the Fed giving money to the US government
Quantitative easing = the Fed giving money to banks
In the case of the US, the entire game is also complicated by the fact that the US dollar has insinuated itself into the global economy. Most critically in oil markets.
Because of this, there are some things the Fed can do (mostly) without the consequences other countries would face.