"[T]here would have been no Dark Side of the Moon, and no dragons-and-warlocks-themed prog-rock epics, had the Beatles not decided to don epaulets for their lark of an album cover and impersonate a vaudeville band."
Well...no. The Beatles were innovators in various ways over the years, but if you're talking about the most significant stylistic "currents" that were flowing in early 1967 and ended up contributing to the evolution of "psychedelic" and "progressive" rock, the Sgt. Pepper album was more of a rider of existing currents than an album that redirected the flow.
As one example, the 2nd half of 1966 was a golden age of psychedelic "dance concerts" in San Francisco featuring LSD, trippy light shows and music by the likes of Jefferson Airplane, The Grateful Dead, Love and Quicksilver Messenger Service.
Because the Beatles were the high priests of pop music (and more popular than Jesus, as I understand it), their 1967 offering was heard by a wider audience than most others. But honestly, if the Beatles had broken up after Revolver, the further evolution of "psychedelic rock" (including the Dark Side of the Moon) and "progressive rock" (with and without dragons) would have been pretty much the same.