Need to play Devil's advocate here BillO; the proof is not in this particular pudding.
The reason for the 1920s/30s routing was, as you say, to accommodate the relatively short range of the aircraft involved (and incidentally goes some way to explaining the current hodge-podge of middle-east politics, as the British Empire ran roughshod over emirates and sheikhdoms in order to provide an air-route to British southern Africa and to India).
Your Directflights map is not an air-route at all, its a travel agent's illustration of a hypothetical link between the 2 cities, in the same way that the London Underground Map joins Waterloo to Paddington. Its not a navigational map. If you look at a tracking site like Flightradar24 you'll find that the normal route is typically Balkans, eastern Med, Egypt, northern Red Sea, Ethiopea, Kenya, Tanzania, and all well to the east of a Great Circle. The reason for this is to related to common sense as well as insurance requirements; most aviation insurance excludes flight over war-zones, rogue-states and specifically some countries such as North Korea, Libya, Yemen. Hence, very similar to Imperial Airways, in fact, but in hours rather than days, and not a pith-helmet in sight.
I agree 100% with your concept of modern air-routes generally being more direct, but you'll likely be looking at oceanic examples to get your point over. Glad you're feeling better btw.