Simon Wren-Lewis appeals to the history of the past few decades to develop an argument for making central banking less independent. I think there’s a simpler way to put it: good macroeconomic policy typically requires coordination between monetary and fiscal policy. This was true in the early-mid 1980s in the US when very expansive fiscal policy combusted with tight monetary policy to drive up the value of the dollar and require a Plaza Accord to repair the damage. It’s true today, as SWL says, to facilitate some sort of helicopter to fly us out of chronically deficient demand. This is old-fashioned Keynesian economics, the sort I learned in the 1970s, and it still makes sense.
Incidentally, one of the arguments for ICB’s that SWL cites has never impressed me much, that it counteracts the pro-inflation bias of populist politicians. If the rest of the political economic landscape were perfectly neutral with respect to competing policy objectives, there might be a point. But in the world we actually live in there is a politically powerful financial sector in every country demanding hard money at each moment of the business cycle (except of course the crash). This lends a contractionary bias to monetary policy under systems in which central banks are insulated from other political pressures. Obviously, reducing CB independence is not a solution in itself, because politics is often misguided, but if there were truly a soft money bias from electoral pressures, it might take us closer to neutrality overall.