Classic rock (60s and 70s for me) spanned both the flatwound thump era, and the more raspy roundwound sound like the who.
Others here will disagree, but to me, a P-bass will limit you to certain types of sound. The P sound is my go-to (!): that P pickup puts the note out there, no questions no mercy. J pickups are better for dancing around the groove, and soapbars/humbuckers, well I will leave those for others to describe.
Used J basses for years, but always lusted for the way that P pickup hammers-out a note.
I just picked up a Custom '62 P Bass pickup. Ever experience that? I'm installing it on my P Bass that I'm putting flats on.