Just a theory of course. The 'OFF' function seems to work perfectly(same statistics you cite), so the button itself seems harmless enough. It just is ineffective after pressing it when the phone has been 'OFF'. Hence, the 'handshaking' between the 'phone-is-now-OFF' circuitry and the button......OR , 'turn-on' circuitry is somehow overloaded(??) when fully charged and Off??, because, after all the button pushing monkey-motion that Apple uses to do reset-boot-ups, then that circuitry starts to function again- until the next time. Since many/most 16s of the various levels are probably OK, I suspect it is poor circuit board/chip assembly for we unfortunate few- seemingly reinforced by the fact(?) that assembly has changed from China to India, with all the attendant teething problems. To my limited knowledge, none of these types of problems have occurred in earlier iPhones, despite Apple's attempt to project that they have by including the "fix" for models going back to the 4 or 6, or whatever, though I don't think that fix was needed back then, except in rare occasions. It would be nice if Apple sent out to all 16 owners a comprehensive discussion of the problem, their attempts and progress in solving it, and, at the very least, an informed discussion to buyers of the potential for trouble, and the attempts for a temporary fix, and certainly a free fix when discovered, and/or refund. Not unlike an automobile or dishwasher recall, especially from the richest(/) corporation in the world.
I go way back with Apple. They never offered Apple Care until relatively recently- they didn't need to, and gave free help and advice-forever. Maybe it has to do with "portable" products, but certainly, when they began offering Apple Care, their quality started to slide downhill; Steve's passing, company growth surging??? When living in SF area, I attended the first Apple Store the day after it opened, and I will tell you that, back then, the Apple Geniuses, were for-real Geniuses. I've had too many of their fine AND EXPENSIVE products over the years to think otherwise. So, like you, I will be putting Apple Care on my new Air Pods Pro 2, and both of these phones, just to protect myself against the unfortunate "events", with no-questions-asked replacements/repairs. I/m very happy that you have not had any problems so far with your 16.