When I was younger I wheeled Jeeps in extreme conditions. That involves a lot of modding. And it carries over to basses.
Instead of asking why mod a perfectly good bass, I would ask why accept a feature you don’t like on a bass when it’s easily fixed?
Fender used to make a Sting signature bass. No more, so I bought the pickup and mounted on a 54Pish body and it’s pretty damn close.
That’s why you mod.
I can’t answer your other question, I don’t keep up with the Jazz market much. Schecter J4 and Charvel San Dimas jazz with factory DiMarzios is what I’d look at if I wasn’t looking for a bass to install Fralins or JBEs in
I know why you want to mod.
Several years ago I tried getting rid of noise from G&L ASAT (telecaster) US made guitar. It was driving me crazy even though it was the most convenient guitar I had in my hands.
I spent money on pickups, luthier… finally I got rid of it all with a massive loss. I just couldn’t stand that guitar anymore.
I won’t go down that path again.
I can change string brands/types or strap locks.
It has to tick most of the boxes from the beginning. There are some nonnegotiable requirements though. Being noiseless is on the very top of that list (since that f**n G&L Tele).
I have this same problem for some reason. As soon as I’d put something eg. Non Fender into Fender guitar, even if it improved it drastically Id just get rid of guitar afterwards. I just stop liking it as much.
Btw noise is easily fixed with good grouding or noise cancelation pedal.
Believe it or not I can make my Yamaha SBV-550 (P/J) sound as much or more like a classic P-bass than I can my actual Fender P-bass (due to it being alder/maple with a mids-heavy ceramic pup).
As you can see here the P pickup placement is very close to a P-bass on the SBV.