My experience is 25 years playing a 4 string Fender Precision and, so far, 8 years playing a 5 string Mike Lull P bass. No mud in either of those basses. Your post was highlighting the split pickup in particular. It is a humbucker design which should operate the same on both 4 and 5 string basses.
If there is a difference between recorded and live P basses, then that difference isn't the bass or its pickup design, it's the rig and the EQ used.