Well, here is how I think of it. In operational terms, there’s nothing monetary policy can do that fiscal policy can’t do. There might be political barriers that fiscal policy faces and monetary policy doesn’t. But if so, I suspect that’s only because those who implement monetary policy are unelected. On principle I favour working through the political difficulties that arise from the democratic process over eliminating democracy.
I’m not an economic historian, but I’m not sure I believe that inflation has been any better controlled since the 1970s. (Old) Labour governments would always let unionised wages get ahead; Tory governments always let house prices in choice areas spiral out of control. They’re both answering to their constituencies. But by the miracle of indexing, only the former is officially counted as inflation.