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This may sound like Federal Reserve fan fiction, if such a thing exists, but the best thing Fed Chair Janet L. Yellen could do right now might be to say that she'll stay on — even if President Trump doesn't reappoint her.

She could actually do that. Fed chairs have the option to serve out a 10-year term as a Fed governor if they aren't picked to lead the Fed again. It has just never come up the past 40 years, since they've always been reappointed as long as they're doing a good job and want to keep doing it. Indeed, President Ronald Reagan kept Jimmy Carter-nominee Paul Volcker, President Bill Clinton kept Reagan-nominee Alan Greenspan, and President Barack Obama kept George W. Bush-nominee Benjamin S. Bernanke. Trump, though, really might not choose Yellen despite the fact that the unemployment rate is at a 16-year low and inflation is under its 2 percent target. “You like to make your own mark,” he told Fox Business's Lou Dobbs, “which is one of maybe the things she's got a little against her.” So is the fact that he seems to want someone who would take a lighter regulatory touch to Wall Street.

Not all deregulators are created equal, though. Jay Powell, the current Fed governor, who is reportedly the front-runner for the top job, might not be quite as tough on the big banks as Yellen would be, considering his finance background, but it's not as though he would gut the post-crisis rules. Not when he voted for them himself. And just as important, he has supported all of Yellen's interest-rate decisions over the past few years. Powell, then, would be the change candidate for the status quo.

But the other finalist, Stanford economist John Taylor, would be another matter entirely. It's not just that he would probably ease up on Wall Street given that he thinks the government was to blame for a lot of the bad decisions banks made in the run-up to the crisis — a position that, as Bloomberg News's Barry Ritholtz points out, is not borne out by the evidence. It's also that he has consistently called for higher interest rates to fight inflation that isn't there, and has never admitted their mistakes. Instead, he has concocted ever-more-elaborate theories — easy money causes lending shortages and is just about bailing out big government! — about why he was right to be wrong.

Of course, it's possible that Taylor would change his tight-money tune now that a Republican is in the White House. In fact, his supporters seem to be counting on that, albeit put a little more politely. (The Wall Street Journal Editorial Page, the unofficial organ of supply-side thought, argued that Taylor wouldn't choke off a tax cut-fueled boom, because he “believes that faster economic growth without inflation is possible and necessary"). But, you know, it's possible that they wouldn't — in which case, it would make a lot of sense for Yellen to stay at the Fed as a governor.

Yellen wouldn't get to decide what the Fed voted on anymore, but she would still have a lot of influence on how the Fed voted. That's because she has a lot of sway with the remaining members. This, admittedly, is where we enter the realm of central banking fantasy. Since 1993, Fed governors have dissented only four times from what the Fed has decided. Even when they might harbor some private doubts, they tend to be very deferential to the Fed chair. But if someone like Taylor was appointed, and Yellen did stay, we could end up with a situation where there were three Fed governors — Yellen, Powell and Lael Brainard — deeply at odds with a Fed chair who wanted to raise rates much more than they did. Add in New York Fed President Bill Dudley and San Francisco Fed President John Williams, both of whom have generally agreed with Yellen and will be voting members next year, and they might even have a majority. It'd be enough to make, say, Fed Chair John Taylor either compromise quite a bit or else see himself become Fed chair in name only.

This would be radical, but these are radical times. Don't let the 4.2 percent unemployment rate fool you. For the past 30 years, it has taken lower and lower interest rates just to produce lower and lower growth. Putting someone who doesn't understand that in charge of the Fed risks leaving millions of people worse off than they should be. After all, the low-unemployment economy that Yellen has helped to happen is finally giving working-class families their first raises after accounting for inflation since the end of the Clinton administration.

That's worth fighting for, even if central bankers don't usually fight this way.