There is a way around this problem that preserves the Fed's independence. That would be for the Treasury to issue the coin to the public, instead of the Fed, thereby leaving the Fed's balance sheet, and its control of monetary policy, alone. Of course, no one would want a $1 trillion coin. But Gary Gorton, an economist at Yale University, suggests there might be demand for a bunch of $50 million coins.
...just coin (verb) debt- tax- and interest-free United States Notes (not Federal Reserve Notes) and spend them directly into the economy for a new New Deal on steroids to put all of the unemployed employable people to work in solid-paying jobs and train the rest in high-skills needed work followed by employing them too and permanently. Who even needs the Federal Reserve System? We can avoid inflation/deflation without the lazy usurers leeching off labor (real productivity; real wealth creators).
See: Even More On the Platinum-Coin Idea and all of the related links in that one.