I suspect that everyone (Fed, consumers, government) will be relatively content to float around at 4% YoY CPI for the medium-term now that the "inflation overton window" (if you will) has shifted so much.

I can't imagine that policymakers are going to make precisely zeroing in on 2% their first priority given the current market anxiety... but that's ultimately a bridge that will have to be crossed when we collectively get there.