When recession strikes, it's prone to the currency equivalent of "bank runs" where everyone attempts to trade in their paper money for gold at once, causing a drastic reduction in the money supply, rising of interest rates, and the dreaded deflationary spiral. In the face of a recession, you want the opposite to happen.
During the Great Depression, every major currency abandoned the gold standard, and the time of abandonment is seen as being correlated with their subsequent recovery. The U.S. abandoned it for good in 1971 while the economy was facing stagflation and foreign countries were demanding to exchange their U.S. dollars for gold, of which we didn't have enough gold reserves to fully satisfy.
A fiat currency gives policymakers many more tools to stimulate the economy to meet their objectives. Tying your currency to gold limits the extent to which you can expand your money supply. And don't forget that under fractional reserve banking, it's the banks that create most of the money supply, not the Fed.
On top of that you're prone to sudden random money supply expansions due to new mining windfalls, wasting a commodity that otherwise could be put to use in the real economy, and have to deal with the increased transaction costs of shipping and storing physical gold.