then why does the neck pickup of a Jazz bass always sound like a neck pickup, regardless of the fretted note?
Ditto for the bridge pup. Do some of you believe that if you play high enough on the neck, the 'sweet spot' will move, presumably toward the bridge, and so the bridge pickup will start to sound like the neck pickup? Silly, right?
It's all about the distance from the bridge- not the location on the scale.
I don't think I would grant your initial premise. IME, a neck PU in fact
doesn't always sound like the neck PU, regardless of fret. It's not silly at all. I've done this experiment (albeit with a guitar rather than a bass), and it's true. When you go high enough on the neck (assuming your fingerboard and the neck PU positioning will let you do it), you can make the neck PU sound more trebly than, or at least as trebly as, the bridge PU.
It's NOT all about the distance from the bridge. It's about the distance from a point where the vibrating length of the string stops--a terminus, if you like. A vibrating string has TWO termini, not just one--the bridge and the fret (or not if the string is open). A PU that's close to
either end will sound brighter and treblier than one that's not, all else being equal. The amplitude of a string's vibration is greater in its middle and less at either end. It's about whether the PU is closer to the middle of the vibrating length of a string or closer to one of the two ends of that vibrating length.
Now, it's true that on some basses, the FB isn't long enough for you to get as close to the neck PU as the bridge PU is to the bridge. It's also true that most of us don't spend a ton of time in the very highest reaches of the fingerboard, so what concerns us most is how things sound between, say, the nut and fret 5 or 7 or 9. But that doesn't change the basic mechanical issues involved.