I've always believed that in a CRPG, the entire party should be involved in all dialogue. This means, all skill checks required in passing dialogue checks should incorporate the party's highest proficiency. Obviously, this can be implemented narratively as PnP RPG's and even some other CRPG's do (eg. Wasteland 3), with the most proficient interjecting into the conversation, and using their role to determine the outcome. The swarthy bard uses persuasion, the sly rogue uses deception, and the slaughtering fighter uses intimidation during conversations to try to succeed checks. In a co-op RPG, this is a necessity. All players and their characters should have an influence on the conversations. Not just being able to see the conversation, but using their ability checks to past dialogue options too. Also, in co-op, all dialogue options should use a vote system. Where each player selects their desired response, and the most popular option is used. On a tie, the player speaking has their selection win the vote. But if the choice requires a proficiency check, the player with that character with the highest proficiency wins the tie. That's the simplest and most immersive way I can think of handling CRPG and even co-op RPG dialogue off the top of my head right now.
