FED chairman is elected by POTUS and confirmed by Senate. With 4y term. That is your say - it is indirect but most (all?) things in modern democracies are indirect. Obviously on top of that there are more soft influences - such as public opinion.
“Elected by POTUS”… You mean appointed... Appointments and public opinion could affect rates in non-democratic countries as well. Anyway we’re on the same side. I just want a more directly democratic influence over the rate