Barter and Persuasion should absolutely not, since even in SP you can approach certain dialogues/shopkeepers differently if you use a different character, and it would make no sense to have everyone involved in conversations that, for example, are meant to exclude them.
Making these abilities group-based would exactly serve that purpose, not prevent it.
If for example one of your party characters has a bad reputation (due to narrative reasons) with an NPC that also trades good stuff and the very same party character is also the one who has a high bartering score you're screwed.
I also can't remember a single event in which it mattered for trading which character you used. The offering is always the same, just the price is different, based on reputation and your bartering skill.
As for persuasion I suggest you read my critique of the dialogue system in the other thread I linked. Currently, no party character is excluded from dialogue in SP, quite the opposite. I'd really like Larian to change that. And making persuasion a party-based ability would only support such a change. But I agree that persuasion is a special kind of breed that heavily depends on the question how Larian will deal with the whole dialogue system in SP in the long run.
The basic point is though that in SP you always control the whole party and you usually try to make a party with characters that complement each other. That works pretty well for combat, but not for most social abilities. They are either not compementary (persuasion) or they lead to a lot of unnecessary and tiresome micromanagement (lucky charm, bartering) or they even make combat gameplay less fluid and intuitive and more tiresome (loremaster). I think the game's ability system in SP should make the player's life easier and focus on the fun, not make it harder and force the player to deal with extensive micromanagement for no real benefit.
