"Whether or not regions outside the focal plane appear sharp...that's DoF" - That applies to your eyes, not the original image.
Yes, it still applies to the original image. Tell me...how do you calculate your (incorrect) concept of the "DoF" of 'the original image'. I'd like to see the math behind that, if you could share it. Also, what do you even call THAT THING - because it's not the DoF, by definition.
Regardless, while a tree falling in the forest with no one around to hear it does, in fact, make a sound, a photograph without someone to look at it is a completely meaningless collection of 0's and 1's or an equally meaningless collection of developed silver halide grains in an emulsion. The moment someone views it, all of my points about CoC apply...and that, for all purposes relevant to photographs, is the real end of the discussion.
Imagine that you are a cyborg and you see the world through cameras instead of eyes. One camera has 8mp APSC sensor from 20D and another one has 21mp FF sensor from 5D2 (yes, it's weird, you must be made in China, or something). Both with 40mm f/2.8 lenses. You see everything in clearest details up to a single pixel, all of them, all the time. FF camera has 60% wider FoV, but with both lenses focused at the same distance you would see that they both produce the same DoF.
This is a very simplified concept (no need to tell me that), because I don't want to waste any more time on this, but it is real and correct. That's how your camera sees it and renders the DoF. The question is not "How do my eyes deal with DoF?". It is "How the camera does it?". It may not be useful for thumbnails and snapshots, but there is a need for it in photography with extremely shallow DoF and a lot of cropping, like macro (where you can't bring it back if it's oof).