color me skeptical that fiscal stimulus is irrelevant
You wrote: "Simply on the basis that this is the first time anyone really tried that unconventional monetary policy, that QE, and it does seem to have worked."
I suspect that fiscal stimulus would have helped a great deal more than QE. QE, after all, makes loans cheap, but when demand is missing, offering to loan companies money on the cheap isn't particularly compelling -- I think the expression is "pushing on a string."
Creating demand, i.e. fiscal stimulus, by having the government either spend directly, or give money (in the US) to states to spend, is a much more direct path towards getting money circulating in the economy, and increasing V.
And it would "obviously" have helped (well, as much as anything in economics is obvious). We have in the US still too high unemployment, and we also have piles of infrastructure tasks that need to be done, from expanding high speed internet into the hinterlands, to repairing bridges and roads, to hiring teachers to teach overcrowded classes. I suspect it would have been relatively uninflationary to take people who were out of a job anyway, and hire them to do jobs that needed to be done, and that they could have done.
Instead, those people sat on their hands, and the corresponding investments never got made, all due to lack of fiscal (not financial) stimulus.