Flea can only afford 2 (although stacked): Same is true for JPJ from 1962 - 1968 up until the Presence Aera: iconic guitar.com: John Paul Jones - 1962 Fender Jazz Bass And on stacked-knobs pictures don't reveal the settings. My guessing is: most professional players don't use all 3 on full most of the time, esp. not when recording.
For a few years Timothy B Schmit had a signature model Carvin bass. It had two jazz pickups and one volume knob. That was the only knob on the bass. That would lead me to believe he pretty much runs everything wide open and uses the volume knob as a mute switch.
Jones' bass was not a stack knob. The picture at the link is not his "legendary" Jazz, but a much later RI Jazz. His Jazz was a late 1961 model, and by then Fender had changed to the VVT set up. I'll let you see if you can spot the knob settings. However, my input would be - it depends. I doubt he (or anyone) used the same settings all the time.
So anyway, what would be the best all around setting for rock? I'm terrible with the technical/electronic aspect of playing bass.
Really? Not to be an ahole, but is this a real question? If so, my answer is, play around and see what you like. And what you like for one song you might not like for another. You have two volumes and a tone, it ain't "technical". People over think stuff. This is freakin' music, rock and roll no less, just plug in and play and see what happens.
Sorry for not taking a closer look at JPJ Jazz! I think it is really important not only to listen to the bass on its own and find out, what setting you like, but to listen to the bass in context. Many people like the humbucking and kind of out of phase effect you get when you have all 3 on full or on earlier Jazz Basses the neck and bridge volume at about 70%-80%. You clearly hear when the "phase out effect" sets in. This gives you a kind of boost of the lows and highs and a cut the the mids effect. Good for slapping for example. As soon as you set one volume lower than the other, you get more noise (the humbucking effect doesn't work) and the sound might not be as pleasing at first sight, but it works better in many contextes. The 3 on full sound often gets lost in a mix. The most important but most difficult part of the bass IMO are the mids. Everybody likes a clear high-end and punching lows at first sight. Mids are much harder to reproduce and can be unpleasing but they define the sound and give it character. Although not a Pastorius fan I like the soloed bridge pick-up with the tone set to cut the treble (as shown in Pic 3 if I'm correct) and the other way round: the neck-pu much louder than the bridge pu (as shown in pick 5 and 6).