The idea of party face characters should die in a fire. Not just any fire though. Like a dumpster fire. The idea that an entire class of challenges that have a pivotal impact on the course of play and can be lengthy and involved should be entirely in the hands of a single player while the other players sit back and watch it happen is antithetical to what I consider good play.
If every social interaction had to be handled by the Face, then, sure, that would be a bore. Just like if every battle had to be handled by the Beefcake and every puzzle by the Brain. With that said, though, I can't think of a group I've played in where we didn't develop a sense of who-would-be-best in various situations. We don't send the scholar to the front line in a fight with the troll. We don't ask the barbarian to pick the lock on the casket of jewels (though we might ask him to bash it open). Similarly, although all of the characters role-play during social scenes, if the stakes are high, we will usually depend on the most diplomatic character to do the bulk of the negotiating because it gets us a better deal. That has always seemed fun to me. And, of course, depending on circumstances, we might use a different Face. In my GURPS games, we commonly see three different types of Faces, the high-status negotiator, the terrifying intimidator, and the streetsmart underworld person. Sometimes these are combined into one character; sometimes not. I've seen bards excel in all three roles in various combinations.
Hmm. I like having some sort of mechanic for social interaction. For the same reason we have a mechanic for settling combats rather than having the players punch one another.
I agree. As with combat, player skill can be rolled into this if that is the group's preference. With combat, players who have a better sense of strategy and tactics will often have an advantage, even if these skills are not represented in the mechanics. In social situations, glib players who pay attention to the social dynamics of the setting might have a natural advantage. More detailed mechanics can mitigate this and can allow players to play characters who have expertise in areas where they don't excel. If a player with little interest in military strategy and martial arts wants to play a skilled combat leader, we can represent that with a mechanical skill. A socially-oriented character, like a bard, might have skills that represent empathy, social awareness, etc., that help the GM provide tips to an otherwise clueless player.
As for setting - I agree with all the above who've said that the setting will have a major effect on how we see the bard as effective or not.
I would hope that a GM who intended to entirely nerf a class would just ban it outright, or at least include that information in their session zero notes. I've run games, for example, where magic was severely limited, but still allowed players to choose a magical character. They knew, going in, that they were choosing the "hard" skill-level for the game. If I had dropped the bomb on them mid-campaign, that would be no fun for any of us.
In most games that I've played, whether 5e or various GURPS flavors, the bard concept has worked fairly well. I even know of a group that was entirely composed of bards!