I started out as a musician in the late '60s and the Hammond Organ sound was essential (I'm a long time keyboard/sax/flute guy - I'm recently learning to be a bassist). Then when synths became common - in particular the Yamaha DX7 -- when the DX7 came out and you could get a bunch of sounds that, at the time, we thought were pretty close to "the real thing", everyone sold off their Hammond Organs and Fender Rhodes and Hohner Clavinets and Mini-Moogs for dirt cheap (I used to pay $200 for a Fender Rhodes and $50-100 for a clavinet and about $150-200 for a Minimoog during this period).
This example isn't a perfect fit for the P-Bass question - because there was the lightweight ease of carrying a DX7 around vs carrying the standard B3 plus leslie cab, Fender Rhodes plus twin reverb, Clavinet and Minimoog ... but the point I wanted to make is that at the time, we all thought the DX7 sounded pretty good. But after a few years everyone was sick of that sound -- and the sound of a Hammond B3 played through a leslie just continues to be "the sound" after all these years (since about 1939 or so). And that is my point - there are lots of basses that sound "better" (more tonal options, brighter, louder etc.) but that sound quickly goes out of fashion and the sound of the P-bass does not.... that P-Bass sound will still be "the sound" 50 years from now.