Curiously, the same point has been made by Howard Haycraft in an article entitled "The whodunit in World War II and after" (collected in The art of the mystery story, 536-542). In this article, Haycraft also points out that the number of new (British and American) published authors decreased radically during WWII. Thus, the popularity of mystery fiction during WWII was essentially due to a prolific establishment of writers whose creativity was then in full-fledge.
I have often thought about this issue, and suggest that the explanation of the phenomenon you mention lies in this: such an establishment of writers didn't exist during WWI.
Not only there were much less popular mystery authors to start with, but the vast majority of them were already past their prime and must even then have been perceived as something of the past, when compared to emerging writers such as Chesterton, Bentley, Mason or even Philpotts; these, in turn, were too recent to be contemporarily perceived as immediately significant; they would form the basis of the post-war mystery establishment, but weren't already part of it. One only has to think about writers like Morrison, Ottolengui, Orczy, Jenkins, Meade and others to understand this clearly; your beloved Freeman is, I believe, the exception rather than the rule.
The war-time decay in publishing by typically pre-war authors (by this I mean the ones that conformed to pre-war conventions) must have been caused not only by the war itself (according to Haycraft, the number of published mystery titles has also decreased during WWII) but by the progressive creative exhaustion and old fashiondness of most of those writers. Time would confirm this: after the war, only a small number of typical pre-war authors have continued to produce significant works; the next years of mystery writing would be dominated by the new school of direct heirs of the writers I mentioned above.
Of course, the decadence of the pre-war authors alone doesn´t explain the almost complete disappearance of the mystery story in English speaking countries during WWI. This factor, nonexistent during WWII, must be combined with another one: the non-emergence of new published writers during the war. As I mentioned, the same seems to have occurred during WWII.
This may be explained generally by a natural retraction of the publishing market during the wartime effort. But one could also point out that the formal artistic changes (from the short-story to the novel) that were taking place in the mystery story at the outbreak of WWI also demanded significant commercial changes in the publishing industry (from magazine to book publication). So, the market was also in a transitional period, and the accomplishment of this evolution would have been virtually impossible during the war.
That the issue may well have had a commercial aspect to it is suggested by the fact that such an important book as The mysterious affair at Styles has been written in 1916 but published only in 1920. The lack of a market for the new kind and format of mystery fiction that was being written at the time may have discouraged a number of other authors from writing at all. Significantly, Christie only wrote her second book after the war (and after she published her first).
So, I don't think that WWI properly killed the mystery story; WWI only delayed the transition, which was already in motion, from the Victorian whodunit to the inter-wars fair-play school of writing. In other words, it has only delayed the inevitable birth of the new mystery story.
But of course this is only my own view on this complex subject.