Hmmm, i own several basses, as i'm sure many of you do. i just received this less than 24 hours ago:

AVRI '64 (sorry, another 'p' pic)
It came with flats. I plugged it into a vintage Acoustic 126 combo (1x15) and heard some of the most convincing bass guitar lows in recent memory. I typically string all my basses (a wide variety of types) with round wound DR's, LaBella's, Dean Markley's etc. It literally never occurred to me to try flats (since the first wave of Rotosounds landed in my world around '70-'71).
I was pleasantly surprised at the richness and tonal color of the factory flats on a p-bass. I conclude that as much as 33% of tone comes from the type of strings employed. Rounds give a p-bass more 'grind' and flats would give a Ric more thump.
Entwhistles P-bass tone in '69 when i saw the Who perform Tommy during its debut tour was more grind-y (round wounds) through his dual Hiwatt stacks, but never lacked bottom. In fact it struck me as glorious tonally. This was in Detroit's Grande Ballroom about a 1-2000 head venue.
I could certainly qualify for the No P-bass club with my 9 or so non P's. It's my love for the 3 P's that ruins me (lol).
I must admit right here in front of all that the bass love of my life was a 66 P.
Cheers and good times to the 'P' free zone.