Never carry a pistol while bowhunting. And I've never needed one. I encounter a lot of black bears each year, at close range (last year I could've poked a sow and 2 cubs with my bow, and this season I saw 8 bears in one afternoon on the same hillside). And we rarely see a puma, but know they are here from their sign.
Part of being a woodsman is understanding animal behavior, and with bears most situations can be peacefully de-escalated with the proper body language and reactions.
If I was in grizzly country I'd carry bear spray. I did like what Mike Mitten said in one of those recent podcasts, something to the effect of "...if I needed to I could hunt with my handgun and I can't hunt with bear spray..." That is a good point. But he is talking about long trips in big wilderness and survival.
From the perspective of personal safety I think a handgun could be more of a liability than protection in a lot of situations. You pull a gun out on a cartel grow site around here and you're gonna disappear. You try to shoot a bear and just injure it, and you might provoke an attack that was never going to happen.