Except this isn't how the Fed has functioned for three decades now. In most cases the fed is acting as a surrogate for what congress and the president wish to see happen. The notion of independence is tenuous at best.
If the Fed was responsible for LONG TERM decisions then they wouldn't have focused on monetary policy which fostered gross debt accumulation as a means of growing the economy from the 80s onward. Nor would they focus on liquidity injections to solve a structural economic crisis.
There's nothing really wrong with the Fed as an entity. The problem with the Fed is usually the people piloting the ship.
Not necessarily. During the early years of the Reagan administration, Paul Volker was chairman of the Fed, and he notably did not particularly concern himself with what Reagan or Congress wanted. Which is why Reagan choose to appoint Greenspan in his place. Greenspan, on the other hand, was the choice of Wall St. And what Wall St wanted, not what Washington wanted, was what Greenspan did. Now many in Washington may have benefitted from that or gone along with it. But the truth is that for the most part Washington did not understand what Greenspan was doing. And Greenspan was extremely secretive with Washington. He deliberately obscured what he was doing, and why he was doing it, from Congress and the presidents. So as long as Wall St kept insisting that they wanted Greenspan, Washington kept giving him the job again.
So it isn't really fair to say that the Greenspan Fed served current politics. However, it is fair to say that the Greenspan Fed was a Captured Regulatory Agency. So the Greenspan Fed was not doing, in your phrase, "acting as a surrogate for what congress and the president wish to see happen." But rather what Wall St wanted to happen.
Now both of those possibilities, lack of acting as politically independent, and regulatory capture, are real dangers to be aware of and avoided to the greatest extent possible. And the way that you avoid them is in greater knowledge on the part of elected officials on what the agency does, and greater care that it does it as intended. If it had been me in office, for example, I would never have tolerated Greenspan's obfuscations.
So the failure was not the failure of a Fed serving current politics. The failure was the failure of the elected government to exercise its oversight responsibility. And that also is a deeper political failure. The vast money in politics now means that what Wall St wants, Wall St got. And what Wall St wanted was Greenspan and his policies.
So you are right that it is who is piloting the ship that is a critical issue. But then again, that's really always true. You can never solve structurally the problem that good or bad government cannot be separated from good or bad people running the government.
For the other parts of your post, you have to understand that the Fed has limited tools to use for often conflicting purposes. And sometimes there is no one right answer. And that is particularly true when Congress is failing in doing its part of the job.