People do that in games all the time in my experience, because they want to succeed, and having the best PC for succeeding in that roll do the talking makes the most practical sense.
They do when there is a plan set in place and the story dictates it. I get that part. But exploration and social encounters are much broader than a combat encounter. A group that's going to set a plan into motion, for example, distract the barkeep with a humorous story while the rogue does something he shouldn't. That is a plan. But...
- plans go awry all the time. Maybe the bard fails, so now the barbarian steps in and starts juggling his axes. Performance check please.
or
- The social encounter is with the group. Everyone talks. Everyone participates - just like in combat. And then, one person says something based on the conversation at hand, and boom, they need to roll. For example:
The group of four walk up to the satyr they need information from.
Bard: Satyr, we have come to ask for a favor, a small favor. A favor so small, that all it will take is a few seconds of your time and a single breath.
The satyr grins.
Bard: Would you please give us the location of that rare tree named Yellowroot?
The DM thinks for a second.
Satyr: That would require several sentences, and that is more than one breath. So, no.
Wizard: We need the location of that tree. It's important. Someone's life is hanging in the balance. Surely you want to help.
Satyr: Help? Yes. You? No. And please don't call me Shirley.
Bard: So you are going to let a person die because you don't like us? Be reasonable.
Satyr: A reason, with reason, is unreasonable.
Rogue:
Sighs. I didn't want to give this up, but I will. What if I give you this bottle of Starfish wine. It is straight from the Captain's locker of one of the most renowned boats that sail the coastline not far from here. I hear it doesn't make you drunk, but rather exceptionally drunk.
DM: Make a persuasion roll.
I mean, seeing that we don't get to watch each other's games, the only thing we have to go on is what games are out there online. I haven't watched a ton, but the episodes I have seen are full of encounters similar to this. The same is true for the exploration pillar. Many times, the best person for the job isn't the one performing the action because circumstances and character motives/impulses dictate otherwise.