Your emphasis on resolution only being relevant at "any given moment" is just grossly ignorant of how displays work. Darin, and others, have been trying to teach you this, but you are stuck in "can't be wrong on the internet in front of everybody mode."
E-shift samples and displays higher resolution than 1080p - double that resolution - by presenting 2 separate frames worth of resolution so fast sequentially that our eyes perceive it as a single frame image. This is no different than how other elements are built sequentially in the same way - e.g. DLP color.
But more to the point, as Darin has pointed out: CRT displays build resolution SEQUENTIALLY.
A CRT quickly scans a frame, one pixel at a time, at a rate fast enough that it appears to our eyes as a single frame presenting all the resolution of a single frame.
So, to use your criteria: "At any given moment".... a CRT is only displaying one lit pixel. Does that mean that CRTs only have a resolution of 1 pixel? Because USING THE LOGIC YOU USE to deny sequential resolution for JVC's E-shift, that's what you would be saying. (1080i also uses sequential fields to create it's higher resolution as well).
Laser projectors also create 2K and 4K resolution by 'at any given time" only producing one pixel on the screen. Look up how they work:
"The systems work either by scanning the entire picture a dot at a time and modulating the laser directly at high frequency, much like the electron beams in a cathode ray tube, "
So, please, try to answer a question directly: Is building resolution sequentially in a way that our eyes will percieve it as a single image a valid method or not? Does it make sense to denote the resolution of a display based ONLY on what information it displays "at any given time" or does it make sense to acknowledge resolutions that are derived from sequential building up of information our eye will see as one image?
If you deny the validity of sequentially-built resolution, then you would have to say CRTs ought to be considered ONE PIXEL resolution displays, and 2K and 4K laser projectors ought to be considered ONE PIXEL resolution displays. This pits your knowledge against the entire industry. Do you want to look that silly?
Or, can you just admit that sequentially-built resolution - how it will be put together by our eyes - is an entirely valid measurement of resolution?
In which case, two different 1080p frames flashed sequentially to appear as one frame to our eyes, amounts to higher-than-1080p resolution (double that). It would therefore be WRONG to consider E-shift resolution (for 4K sources) as only 1080p for exactly the same reasons it is wrong to refer to CRT or Laser projectors as only being 1 pixel resolution. Can you admit this?
(ETA): If your claims about the large gulf between native 4K vs E-shift were correct, then shoot-outs between the new JVCs playing 4K sources and the Sony 4K projectors should produce obvious a differences in clarity and resolution. Instead: virtually every person who has done a shoot out with the new JVCs and the Sonys playing 4K - that includes reviewers, people on this forum, and several public shoot-outs in Europe, ALL confirm the difference is extremely subtle as predicted by an actual understanding of how E-shift and basic display resolution works.
C'mon. You can do this. I know you can.