My guess is that this is some kind of awkward compromise to not always give to the player an easy path to a successful outcome.
Well, the thing is, this is a party-based RPG. Larian made sure to advertise as much. Having a balanced party that can cover most of the bases is part of the point of the game. There's even a loading screen reminding us of the value of a balanced party.
So, it wouldn't make much sense if the designers' reasoning was "oh no, if we let players act like a whole party during conversation, they'll always have good bonuses for the choices they make".
As a result, I don't think this is the core explanation for why conversations don't involve the whole party.
If it worked like that, there would be no reason to pick other options than tagged ones since they are always better choices than untagged ones.
I'm not so sure of that. Because the DC (Difficulty Class) you face when picking an option is not always the same.
For example, iirc, when trying to convince Kagha to let Arabella go, you can use a [Druid]-exclusive dialogue option, or you can try a [Tiefling]-exclusive dialogue option, and the latter has a higher DC.
I'm sure there are some cases where you could, for instance, either use Intimidation and get a DC 18 or use Persuasion and get a DC 12 (because you're facing someone who's not easily intimidated, because the Intimidation line is actually stupid, and/or because the Persuasion option is actually the most sensible given the NPC's situation). And a DC 12 with a +2 bonus is easier to pass than a DC 18 with a +5.
So it would not necessarily be the case that the players would default to "tagged options", or more precisely, the options involving the Races, Classes, or Skills that they have good bonuses for in the party.