For as much as I claim that artists (all of them, Beatles included) have some very distorted and inaccurate view of their own strengths, this seems like a case where everyone's antennae went up at the right time - "Hang on, this one's a bit different than the others, something special about it, let's give it the priority it deserves, etc." Even John's bitterness about "Revolution" not being the big Beatles single of the moment seemed fully tempered by a (fully accurate) sense of "Oh, fuck - 'Hey Jude', there's no arguing with THAT one."
As a song, an arrangement, a record...if you're willing or able to concede that sort of "infinite beauty in a grain of sand" quality to its inherent uncluttered simplicity, it's an absolute motherfucker. Such a simple build - the piano and voice, the acoustic and tambourine in on the second verse, the backing vocals in halfway through that, the drums and bass tumbling in for the bridge, the incredibly spare electric guitar, even the staggering of the strings and horns in the coda* - none of these are sort of "Good Vibrations" tricks of innovation and hard graft, but they are absolutely what the doctor ordered. The "trick", such as it is, is just people with incredibly good instincts having the basic sense to resist "their fancier selves", and...it's as if they managed to deliberately get out of the way of a meaningful musical event.
I've seen the old boy perform it some ridiculous number of times now (you'd either laugh or cry if I named the number), and this seems like (even more so than the others) the one number where the band is especially keen to honor the original arrangement to the letter. It's like building an especially specific Jenga tower or domino arrangement - if you moved one piece, it would collapse instantly.
*The one thing that absolutely belongs to the original record is that very specific sequence of improvisations Paul belts out during the last four minutes. He never did it that way before, he'd never do it again. There's an unrepeatable sanctity to that moment that only serves to make the record more special - you get the gloriously restrained power of the arrangement and execution, AND you get a very specific one time event/celebration. You even get a swear in the last verse if you want it