A big reason why we have a Federal Reserve handle monetary policy is to smooth out the economy over time and prevent recessions and booms.
But interest rates aren't the only reason why economies fluctuate. These days, oil prices are really important--their spike last year is a big and underappreciated contributor to the current economic problems.
The reasons why oil went up that high haven't gone away. Much of the remaining oil is controlled by autocratic regimes with nationalized oil companies, who chronically underinvest in new production. The rest is barely accessible, poor quality crude, in deep sea deposits, or tar sands. Combined with price controls in important consumer areas--the Middle East, South and East Asia--this results in inelastic demand and supply.
And that means huge price fluctuations in energy. But today's economy is very dependent on energy prices--it made the crash worse, then low prices contributed to a quick rebound, and higher prices in the future might cut off a recovery.
That means, as long as the price of oil remains as volatile, America's economy will remain very unstable, and will respond to and drive the cost of oil. Especially now that monetary policy is very limited, being immune from world energy prices would really help stabilize the economy.
And that would require a very different energy source.