On the Federal Reserve's 'Independence'

The Fed is considered to be 'independent' from political influence of the USG and the Congress. But, is that assertion true when we consider all economic actors and political processes?

I do not think that I -as an economic theory agnostic- can consider Fed to be independent from the influence of the financial sector it is supposed to oversee. The Fed may be independent from the influence of Congress but it cannot be independent from the realm of actions of the government, by definition. Ergo, the Fed is an arm of the government but it is paradoxically 'independent of it'. What? Nowadays the Fed has become the 'magic' bullet in terms of economic policy at national, and arguably international, level.

When the government (read the Cabinet and the Congress) cannot promote coherent policies the Fed just magically shows up and lowers the interest rates to close to 0% levels or even below 0% in real terms. Or, 'it purchases' government issued bonds and calls that euphemistically 'quantitative easing'. Or, the Fed chairman has a public appearance where he/she utters 200 words and the entire financial industry deconstructs the entire speech into (in)coherent parts. How is it acceptable that we get no say in the election of any members of the Fed but they have the ability to affect our lives in the most profound of ways? This is as clear of a contradiction of our political tenets as it gets.

We -as economic actors, consumers, and political beings- cannot continue to tolerate an independent -from-the-people central bank authority. This is totally anti-democratic and surely subversive to the entire democratic processes.  When the Fed deliberately debases the currency they are performing nonrestrictive political functions, and all in the name of -possibly- flawed economic theories. How are we supposed to accept that? Since when do we tolerate economic 'noises' in our decision making processes?

Eliminate the Fed and make the Cabinet and the Congress be the only macroeconomic decision makers in our country. Otherwise we have lost our independence and have given up our economic soul to a theoretical construct. The effects of our voluntary abjuration of our macroeconomic powers to a body that only represents theoretical domains are dramatic and we can witness the effects of that as clearly as daylight. What do we see because of the Fed's actions? High unemployment, monetary savings that lose value every day,  assets that are worth less and less over time, negative real interest rates, economic decisions beyond the political realm, and so on.

Our currency is part of our economy and not outside of it and control of the currency should be an inherent part of our government, without much doubt.  We elect the government and we cannot elect the value of our currency our nation issues? How does this make any sense to you? To any rational human being...