The Fed has had this fixation with inflation going back now 30 years to Carter's days of stagflation. The Fed served us up some bitter medicine in the early 1980s and the Reagan revolution paid the price for that in the '82 elections, but it cured the damage done by Carter. But they should have a wider view than just keeping the brakes on inflation. That's important, to be sure, but so is the stability and viability of the overall system. To the extent that the Fed has influence over that, they should use it when tremulous times come.
It's not the Fed's job to bail out banks for lending money out without adequately investigating the borrowers ability to repay. It's not the Fed's job to pay attention to the equity markets. If there is a massive economic slowdown, yes, cut the rate, but it's not needed for this. The market ultimately punishes stupidity.