Currently, I think there's a competitive aspect of using your own character personality for conversations, one that could easily be cooperative.
In a RPG tabletop perspective, the ideal case scenario would be that for every player that participates in the conversation their race/background/class/etc would be added as a conversation option (if available), instead of relying only on the player's that started the conversation, since everyone is present at the "table" and they could easily intervene.
One example would be if a Druid could help dealing with an NPC but he "didn't act fast enough" to talk to this NPC first or was busy doing another thing (which isn't that hard, with so much stuff to do). So, in this idealized scenario, he could later join and intervene through an additional conversation option (if available).
What are your thoughts on this? Am I too far off or missing something?