I still reach for them often, even though I have other options.
Hmmm...that may indicate you're an older guy, Papaw

I'm an older guy, too, and went through a long period of not using them, reaching for the smaller versions of Channellock-type/waterpump-type pliers instead. Of late, I've come to recognize their virtues for small work. There are times when I need to come straight at the work, rather than at an angle, as Channellocks do. And they're more compact; I have a pair on my carpenter's belt (back pocket of tool pouch, off side, which is the right in my southpaw case), chosen for their small size compared to other pliers.
If I had to select a desert island tool kit with a cap on the number of tools, I might leave them out; but I don't plan to move to a desert island anytime soon. Although, unless our drought gets over this winter, the desert island may be moving to me/us.
But, to keep the conversation lively, the pliers whose necessity eludes me is linesman's pliers. I can't figure out what they do that's not taken care of by the list Nola posted in his initial question. I have some, but can't recall the last time I reached for them; and they don't live in the "go there first" drawer in the toolbox.
Bill, ducking and running but with a tub of popcorn in hand