You need an agency to regulate the money supply, and trusting the U.S. Treasury to do that in the face of trillion dollar deficits and $22 trillion is debt is sketchy w/o a gold standard. Having an “independent” agency doing it vs. political appointees at the Treasure Dept. is a better choice. That said I don’t agree with everything the Fed does (2% inflation target, QE, propping up Wall Street instead of Main street, etc, etc).
When Nixon broke the link to gold he did it by simple Executive Order... his order actually said that he was just “suspending” gold convertibility rather than ending it permanently... so apparently Trump could counter Nixon’s E.O. with his own E.O. and we’d be back on the Bretton Woods gold standard.
The pressure on the gold standard back then was due to using the dollar as the world’s reserve currency. An economist named Triffin warned as early as 1960 that this wasn’t going to work, either the gold standard or the reserve currency role was going to have to end. Nixon chose to end gold. It would have been wiser to instead replace the dollar with a basket of currencies as the reserve currency.