For many on Wall Street, a shift away from every utterance of Fed speak and every tweak of verbiage in the Federal Open Market Committee post-meeting statements would be a welcome development.
"As soon as there is some progress on fiscal policy, then there won't be so many people locked in at 2:30 on Fed day to watch a press conference," said Scott Clemons, chief investment strategist at Brown Brothers Harriman. Each quarter, Yellen gives a post-meeting Q&A with the press that is carefully watched on Wall Street.
"The White House and the Hill have far more power through legislation to influence corporate earnings than the Fed does through interest rates," Clemons added. "So, yes, I would welcome that as a more durable driver of equity prices."
The stock market certainly has had a friend in the Fed. The S&P 500 has surged more than 250 percent since the bull market began just more than eight years ago.
However, the rally has gotten new life since Trump was elected in November, with the index up about 11.6 percent since.
If Trump can work with Congress to deliver on his agenda, the handoff from the Fed could become complete.
"It's unclear as to what we'll get, when we'll get it and how much they'll boost growth from a fiscal policy perspective," said Michael Arone, chief investment strategist at State Street Global Advisors. "This dynamic is going to be interesting as it plays out through the balance of the year."
WATCH: One analyst believes the market is getting ready to cool off.