Disclaimer - I own 4 Jazz basses and one P. I would fit an extra pickup to the P if hell froze over. But that's a mojo/vibe thing more than actually thinking it could change the tone if I soloed the P pickup.
As for the body routing for the second pickup or the extra magnetic pull influencing the sound... come on, be serious here. That's almost as silly as the claim that screwing a pickguard to your bass changes the resonance of the body in a way that audibly affects the tone.
As for the body routing for the second pickup or the extra magnetic pull influencing the sound... come on, be serious here. That's almost as silly as the claim that screwing a pickguard to your bass changes the resonance of the body in a way that audibly affects the tone.