If anything gets to ignite a response from me it’s an opinion stated as fact 🙂
I’d agree that simply using a pickup and strings produces a tone that is broadly similar.
Unadulterated Jazz, Precision and Rickenbackers are fairly similar especially if played in a ‘conventional’ mode and manner.
But, many basses have active tone control onboard. I could play my P - Retro equipped Warmoth Precision in a mode that would leave no doubt in a back to back that it wasn’t a standard P bass. Yes I could be wrong, it’d be interesting to see.
Likewise the Zoot ZB1000 in series mode with the active varitone set to one of two or three positions would begin to sound like a different instrument entirely.
In the mix in a rock covers band? Yes it all becomes a bit redundant so long as the bass can actually be heard.
All my opinion of course.
Peter