I agree, at least from a fashion standpoint, if you're going for a throwback/classic look i.e. Motown you don't want a guy up there playing an Ibanez Destroyer.
or, it's possible you've got sound guys familiar with mixing Ps and Js who can't be bothered learning or EQing some instrument they've never had to deal with before, especially if time is of the essence to keep the show moving on schedule. But if you're a Mega star like McCartney or Sting nobody's going to tell you what bass to play. So unless it's someone with a unique styling or voice largely dependent on the instrument itself, my assumption is that Ps and Js simply sound "right" and the players using them normally play them anyway.
Anybody remember when they used to do All-Star Jams at the grammies? Years ago there was one with Stanley Clarke (along with Charlie Daniels, Ricky Skaggs, Glenn Campbell, and a few others I can't remember) performing to a video of Elvis doing "Blue Suede Shoes". (I have it on VHS somewhere). Anyway, Stanley had his Alembic. That's his sound, even though I have no doubt he could smoke on any bass handed to him.