Personally, I care zero about the historical or technical aspects of a P bass. Who made it, when, why, Fender, blah blah blah. No disrespect, and I'm glad someone did, the nostalgia and mythological aspects just don't factor in to anything for me. Just like I don't drive a Ford because it got to market first. For me, a 'P' is 100% about the pickup and tone, not a brand, body style or a neck profile.
All I know is that that split 'P' pickup in the sweet spot sounds right to me, especially when there is a neck pickup to add some versatility on rare occasions. A set of 'J' pickups does not give the same results for me.