I feel that when Gibson started making basses, it asked itself the question "How do we make a bass that is a Gibson?", rather than "How do we make a great bass?"
The result is Gibson guitar body shapes, with humbuckers at the neck and/or bridge. Its a Gibson Bass, but is it the best bass they could have come up with? I am not sure.
Look at Rickenbacker, their bass was a complete rethink and redesign from the guitar line.
While Fender copied their guitar shapes, they quickly adopted a unique pickup system for the P.
I agree completely. While there was much carryover from the guitar designs in both Fender and Rickenbacker's case (bolt on construction and basic look with Fender, mostly electronics with Rickenbacker), there were significant design changes in order to make them work as basses.
The P-bass took much from the Tele, but it's shaped significantly differently in order to accommodate the longer neck.
The 4000 and 4001 share some bits with earlier Rickenbacker models, but they were designed as basses, rather than just being a bass version of an existing guitar model. Also significantly, both Fender and Rickenbacker, in their original single pickup designs, placed the pickup more in the middle of the body (with Rickenbacker's being closer to the bridge), rather than right up against the neck. This resulted in a more balanced tone that did well with the amps of the time and worked well in the mix. Later, when Rickenbacker added the second, neck pickup with the 4001 model, they put a low-cutting cap in the signal for the bridge pickup to keep things from getting too muddy (and too hard on the speakers of the time).
Why did Gibson initially use a single pickup, right up against the neck in their basses, resulting in so much low end that it didn't cut through mixes that well and killed speakers? Well, look the single pickup acoustic/electric jazz guitars they made earlier. Where's the pickup? Right up against the neck. As mentioned earlier by someone, Gibson wanted their basses to be more like upright basses in sound, as well, so they wanted lots of low end, and were, as mentioned, slow to embrace the new rock & roll music of the time, unlike both Fender and Rickenbacker.
While Gibson EB series basses were somewhat common in the 60's, as things got louder and louder, the fact that they didn't cut through well may have become more of a problem.
Fender basses, on the other hand, worked just fine in a loud mix. Same with Rickenbacker basses, though very different.
And of course, both Fender and Rickenbacker have seemed to spend much more attention on the bass department than Gibson does.
Gibson has produced some great basses, and the T-bird has proved successful (though it might be moreso if they'd never discontinued it). And to be fair, they probably sell plenty more basses than Rickenbacker does. But they sell many many times more guitars, whereas the with both Fender and Rickenbacker, I suspect the numbers of basses sold and number of guitars sold are a lot closer than they are with Gibson.
Which isn't to say I don't like Gibson instruments. They make my favorite guitars, and some really cool basses. But their approach just doesn't seem as bass oriented as other companies.