It sits in the mix incredibly well in studio or live. That's its claim to fame.
In addition, so many early records were recorded with the P that our ears have grown accustomed to the sound and many associate that sound as being the sound of an electric bass.
The younger generation has seen and heard more choices growing up - so they're not locked into one brand. But many are still discovering the qualities that made it so popular in the first place.
This.....I have 10 basses (8 electric and 2 semi-acoustic) and 2 of them are (Lakland) basses with P pickups...they just sound so darn good in the mix.....I use my active basses quite a bit as well, but the P does sound "special"
one of mine has vintage pickups and the other is more "modern sounding"...just love the way the vintage sound blends with the other instruments.
also - as is stated above, I grew up with that sound...