Apparently the logi behind such ridiculously low rates is injecting so much money into the system that a good deal of it is passed onto households and businesses at a reasonably low interest rate.
But there is one big problem: the Fed doesn't loan to private people, not even to companies... only to banks. And banks worldwide are right now not conceding almost any loans to almost nobody. And it's not a problem of money availabality: it is a problem of panic, after being overly indiscriminate with credit for decades, they have suddenly panicked and do not want to give any credit that does not have absolutely all guarantees. It's not that they don't have money to loan, it's that they fear to lose it and prefer to keep it locked.
So the Fed would do much better changing its directives and directly giving credit to the people and business, who right now can't get it from the banks. They could even ask for a much higher rate. That would of course be a virtual equivalent to bank nationalization... but in the mid run it's something they will have to do anyhow, because if banks do not fulfill their role providing credit (not mad credit as they did before but certainly normalized reasonable credit), they will need to be scrapped or replaced by some effective economic mechanism, private or public.