The Fed chair is appointed by the President and confirmed by the Senate. It's arm's length, to be sure, but I don't think most people would want too much more direct involvement.
The people, generally, have no understanding of monetary policy either in theory or practice. It's a good thing the Fed isn't at the beck and call of the people.
So, we surrender monetary policy to the bankers and just pray they don't do stuff on their benefit while fucking us?
That's exactly how we got here, in the precipice of a financial crisis that everyone is pretending not to see so we can keep the ponzi scheme running a bit more.
The people have no understanding of a lot of other stuff. That's why we use a REPRESENTATIVE democracy system, not a direct one.
Is it perfect? not.