The Fed is an institution staffed by unelected, career technocrats. It's not supposed to have such sweeping powers (and, by charter, it really doesn't), but, like most parts of the executive branch, it has expanded in scope over time due to a steady erosion of our lawmaking institutions.
Put bluntly, the Fed can do what it does for the same reason the President can start pseudo-wars without going to congress: it's inconvenient for lawmakers to cop to such responsibilities. The other branches of government are simply shoring up the holes.
To be honest, I like the Fed a lot... In so far as grossly unchecked power goes, we could have far less competent people at the helm (The fact that so few in monetary policy wind up in congress is the real tragedy, if you ask me). That being said, future performance is no guarantee. History shows that it is not so simple to take back power once ceded for the sake of expediency when it is no longer convenient.