I wonder if the new horse notices the bleached bones of the old horse when it gets tied up for whipping?
Nevertheless, why not? Having gotten my first P bass a couple years ago after 30+ years of playing J or other 2-pickup basses, I notice (especially on gigs) the greater control and ability to make fine adjustments a J bass gives you. A P bass gives you what it gives you, deal with it or try to do your EQ at the amp. It's a one trick pony. But it's a pretty cool trick, and there are some things for which it's the perfect thing. Nevertheless, I'll take a J bass, (an active/passive one) for the versatility to adjust to the room, mix, and so on, on the fly with bass/treble and pickup blend.
I've kinda been curious what a P bass with an active pre- (with bass and treble controls, maybe even mid control too) would be like, to give control over EQ while still utilizing the P pickup and dimensions. Purists would say that aint a P cuz it doesn't have 2 knobs... I'd say essence of a P is the pickup and location of it.