I agree with the OP and admire the clarity of his argument.
This has me wondering about the phenomenon of what might be called What The Hell Is Going On Here? television series. I can think of only two that were resolved by something other than the supernatural; what might I be missing, here?
Twin Peaks had the demon/ghost/whatever Bob, who could jump from person to person, and who liked to murder people as the solution to the show’s central mystery.
Lost had, as mentioned above, some sort of Purgatory for the dead characters who only thought they were alive. The progenitor of the Character Only Thinks He or She Is Alive plot is, of course, An Occurrence at Owl Creek Bridge: the 1890 Ambrose Bierce story that inspired a million modern stories. That story contained no overt supernatural elements. But to explain how more than one person could have the same shared experience (of thinking they were alive when they really weren’t)–well, that might well necessitate an introduction of a deity or some other mystical explanation.
The UK Life on Mars/Ashes to Ashes had deity/heaven/angels/purgatory/etc. as the explanation of What the Hell had been Going On.
The first season of American Horror Story had ghosts who could kill people (because they wanted them to join them) as the explanation of What Was Going On. (I haven’t seen the other two seasons, but assume that the supernatural was involved in them, too.)
The *'What’s Going On Here?" *series Quantum Leap, Dead Like Me, Pushing Daisies, and Carnivale, all had supernatural explanations (or elements, in the case of those that didn’t fully explain what had been going on). The same may turn out to be true for currently-in-production series such as Under the Dome.
The two shows I was thinking of as being those that explained the odd goings-on in some way other than the supernatural:
The Prisoner (could have been mental breakdown or could have been actual government actions) and the US Life on Mars (pure science-fiction explanation, plus ‘coma-dream’.)
Keeping it just to television series: does it seem to others that the supernatural is resorted to more often than any other explanation, for “puzzle/mystery/mind-screw” shows?