Used to Precision bass-my improper technique prevents me from fully taking advantage of Jazz basses. On a PJ it's different-do not currently have one, but could enjoy it without altering my right hand finger work. Do not know how to use a pick (harder and slower/clumsier than fingers at this point-not being anti-pick). It is not a flaw with the Jazz Bass itself, but with my way of playing-it is likely perfect for 99.9% of everyone else.
I admit I *could* play any 4 string bass, just does not feel the same due to lacking the finger feedback of a "ramp"-a Jazz with an installed ramp would be fine. I do use humbucker basses without issues, as I can use these more easily as "ramps". I also enjoy playing over the fingerboard, using it as a ramp as well for deeper tones.
Due to the scooped sound, the Jazz can sound nicer to many, but I do prefer the mid-rangey and "honky" tone of the Precision-which again, is just what I am most used to. But Jazz basses honestly have a great tone for thousands of musicians. Blame the bassist, not the bass (my issues alone.)
Some music loves Jazz basses. But anything can work, if one puts in the work.
(Right now I do not need more basses, but wouldn't mind a PJ, or a J with a ramp.)