I know it's a TalkBass tradition to say that a PJ with the J pickup turned off isn't a P. I've never agreed with that. Every PJ I've ever played sounds like a P bass with the J pickup turned off.
In my eyes (ears?) a PJ is a P with more options. Some people don't want the extra controls and options, which is 100% fine! Often times, simplicity is key. Or maybe you like wide P necks, that's awesome and I hope you enjoy it (most PJs have a J neck).
Adding a pickup to the circuit that is completely turned off won't change the sound. Sure, an extra route in the body for the J pickup might change the output in a literal sense (physics or whatever), but it's completely negligible IMO. Strings, technique, etc. etc. are going to make a difference before something as silly as that.
I like being open minded, I really do, but come on. I know purists are purists but there's a line. I'm sure someone here will argue they can a difference in pickguard screws.
I see value having all 3 of those basses, simply because some gigs may need the tone of a J, the simplicity of a P, or the extra tonal door that a PJ adds to a P. If I had to get rid of one, though, it would be the standard P for reasons I mentioned above.