If I found gold that was abandoned 1000 years ago, I could sell it because it would be worth something. If in 1000 years someone finds a box of Federal Reserve Notes they would likely not be worth much.
1000 years from now we could be primitive barbarians hitting each other over the head with an antelope's thighbone due to a total thermonuclear apocalypse as we scrounge for unopened cans of dog food.
Plus, it isn't like gold based currency is a clear path to stability. Just look at the fun the Roman Empire had with keeping a stable currency.
(Good clean fun with Michael Parapinaces! Parapinaces was Greek for 'minus a quarter'. In his efforts to pay the army he devalued the currency so the coin -nomismata at the time IIRC- was worth only 3/4 as much as it previously was.)
The Fed didn't prevent the Great Depression, the current financial crisis, or the many smaller recessions that have occurred since 1913. Inflation helps the rich but screws over the poor and middle class.
Let's go through this one by one, shall we?
1) The Great Depression occurred when our understanding of fiscal policy was primitive and monetary policy was the theoretical equivalent of the glint in the milkman's eye, putting it bluntly. The understanding of the role the Fed would play then was vastly different from what it is now and even if the Fed had decided to take an active role in averting/resolving the Great Depression it is questionable as to whether they would have had any tools that could have done it effectively. My economic history is a bit iffy but I'm not sure they had fully worked out the link between interest rates and investment yet.
2) The Fed struggled in this GFC because their primary tool, fiddling with interest rates, wasn't going to work here. Interest rates were already quite low and going any lower could have had some Interesting Implications, things you generally want to avoid. Secondly, one of the core causes of the GFC was a complete failure of the regulators to keep the banks in check, not a task for the Fed.
Lastly, the Fed had decided to take a relatively hands-off approach to monetary policy and were way too concerned about the possibility of inflation even as inflation remained at near-record lows and some indicators suggested we might have been heading for a Japan-style 'lost decade'.
3) The goal of the Fed isn't to prevent recessions, that would be stupid and undesirable. The goal of the Fed is to maintain a stable money supply that accommodates macro goals, whether engaging in expansionary policy to stimulate growth or contractionary policy to reign in growth. When compared to recessions and depression before the Fed was created, recessions and depressions since then have been far more mellow. The troughs are smaller and the effects are nowhere near as catastrophic.
Prior to the Fed we were seeing massive crises every decade or so. After the Fed, we really have seen only three: The Great Depression, Stagflation, and the GFC. The first two occurred before the good monetarist ideas were synthesized with accepted Keynesian conventions and the last one occurred in a situation where Fed short-sightedness both limited their tools in preventing and resolving a recession.