I think it's funny that they put the bigger neck on the smaller body Precision, and the thinner neck on the big body Jazz. Maybe it just balances out karma wise? LOL
I think those two things were coincidence.
I think when Leo (it was Leo I assume) created the Jazz bass he wanted to improve on his first basses.
And those two things (neck size, body size) are unrelated.
Neck: skinnier, smaller string spacing... like said many times before easier for guitarists wanting to play bass.
Also I think that the bass guitar (and people playing it) gained more respect as a worthy instrument. A desire from people in the music world that more technical things could be played more easily.
Making the bass guitar moreso a bass version of a (regular) guitar. To be in the same league.
First Jazz Basses were called "Deluxe" in regards to a Precision Bass IIRC.
Body: maybe a myth or maybe not...
Bigger body usually means better more defined tone. When the wood is the same.
And the offset waist was just aesthetic. To make it look more sleak.
Same can be told about pickups and their configuration. Being captain obvious here: two is more versatile than one.
Because of two single coils can do hum cancelling, there was no need anymore for a split-single coil.
It was not the engineering goal to make a distinct sounding new pickup... but to everyone ears the jazz pickups sounded different.
So: thinner neck for better playability, larger body for better tone. In theory.
That all being said... my perception of it, I still prefer a precision bass.