"One of the most important decision-making bodies in the world" is quite a statement. This is part of what the group who makes the nominations want people to think, no? Do we really have great evidence that the world would be so much different if the interest rate were set 1% higher or 1% lower?
The Fed serves an important purpose: it helps to ensure that there is always a reverse army of labor so that worker wages can not keep up with productivity gains. As for independent institutions in government, we should have none of them and no government.
Cool.
That said, we should have many more independent organizations making up government. There are better ways to organize things that could improve outcomes and prevent dictatorial tendencies.