"Nothing is an improvement on a J-bass" with the moving goal posts of body shape, pickups, bolt on necks, 4 strings, 34" scale etc.
The bass guitar wasn't Leo Fender's crazy brain child that came out of a vacuum. The body shape looks pretty much like a guitar, which isn't too much of a stretch from viol/violin family instruments, which have been around for hundreds of years. Bigger lower bout, a waist/"c" bout, smaller upper bout. On the viol/violin family, that shape was decided upon to provide an acoustic I am fully aware of the. resonating chamber, and to allow clearance for the bow so it didn't stab the body of the instrument. On acoustic guitars (which were around long before electrics came around) it made it so you could play the instrument sitting down over your leg. Ever try to sit with a flying V without a strap? doesn't work so well. The upper horn on electric guitars was extended to balance the instrument and prevent neck dive, because of the solid headstock and heavy metal tuners. The reason that you don't see too many radical shaped instruments that deviate from "generally guitar shaped" is because ergonomically they work. You don't see too many cars with 7 wheels either, because 4 makes sense. That doesn't mean there haven't been improvements since the Ford Model T.
The same can be said about pickups. The two pickups on the J bass have significantly different sounds because of the distances they sit from the bridge. You can get a huge range of tones out of an instrument by soloing either one or blending them, which is nothing new. Archtop guitars had two pickups on them before Fender came into the game. The P bass pickup being where it is gets a particular tone, same with the Music Man/Stingray and its distinctive sound. And there is only so much real estate between the bridge and the fretboard, so it comes as no surprise that other manufactures are going to put pickups somewhere in there.
Bolt on necks: Ease of construction/mass production. Cheaper material/labour costs than neck through or set neck. It works.
4 strings: 95% of the double basses out there have 4 strings. They happen to be (usually) tuned the same, which also happen to be the bottom 4 (bass) strings of a guitar.
34" scale: Compromise. The double bass has a string length of around 42" which most guitar players would find insane and no one has an arm long enough to play that seated. The typical 25.5" guitar neck wouldn't work because the strings would be way too floppy. This has been "improved" upon countless times with 35" 5/6 strings, 30" short scale, fanned fretted basses that have a longer scale for the lower strings that need it and shorter scale for the higher strings.
"Rich musical history"
The P bass hit the market in '51. The J bass in '60. That is 64 years, (55 for the J bass) when music has existed for millennia. Yes, in the west the farthest we tend to go back seems to be Baroque music that started around 1600 because that is when musical notation started to resemble what we are familiar with today, but there are plenty of people alive today that precede the electric bass and it's "rich history". I have nothing against the music that has been made with the electric bass, but it is one of the youngest mainstream instruments around today and people are still coming up with new things to do with it all the time. Suggesting that Fender has some sort of lineage, tradition, or history beyond when other players came on the scene is pretty narrow minded when the Hofner 500/1 ("Beatle bass) came out in '56, Rickenbacker 4000 series started in '57 and the Gibson EB-0 was '59 (before the J bass) and the Music Man StingRay hit the market in '76, and G&L came around in the late 70's. Sure they might have had more popularity initially, but they weren't the only bass in the game.
That turned into a novel. Long story short: Fender P and J basses are considered "standards" much the same way that a four door sedan is the standard automobile. Most other basses look/function similar because the Fenders themselves weren't crazy deviations to begin with, and their "history" is as old as Mr. Potato Head.