This just doesn't make sense. So there is no power cord that exists today or could ever exist that would be safe to run in-wall? I would think that the NEC has spec's/standards that in-wall wire has to meet and if it meets those specs then it is safe to run in-wall. And how do I know that the power cord does or does not meet those spec's. All of this may be answered if Rickster answers my first question.
Even though this is getting a little weird; I'll take a stab at it.
NEC 400.8 (Uses not permitted)
(1) as a substitute for fixed wiring of a structure. (2) Where run through holes in walls, structural ceilings, suspended ceilings, dropped ceilings or floors...... you get the idea.
The code views extension cords as temporary. So much in fact; that holiday lighting cords can be in place for no longer than 90 days. I'm not saying the Xmas light police will show up at your house on the 92nd day, but that's how the code reads.
This just doesn't make sense. So there is no power cord that exists today or could ever exist that would be safe to run in-wall?
Power cord manufacturers know the part of the code that pertains to them; knowing how cords are ruled on, they wouldn't re-invent the wheel. Since in-wall use is already covered by other types of wire.
I agree the code has some quirky parts.- i.e. Federal installations are exempt from the NEC.
Back when I took my code classes, it was on an Air Force base. Since my instructor worked on the base for 30 years; he would walk us around and see if we could find all the code violations. The biggest, was seeing million $ CNC machines powered with S.O. cord.

Hope this helps.
Rick