A ready check for every dialogue? That would get annoying pretty quickly. The game already tells you that's "there's an interesting conversation nearby" for key story elements. If it's something you want your co-op players to hear/see, speak up and let them listen in before continuing.
The roll-off gives me flashbacks to the DOS rock, paper, scissors system. A roll is a slightly different mechanic, but gives the same result. The game already has the option for co-op players to suggest lines, without taking over the conversation.
In terms of role-playing, I don't really agree with the 'face' mechanic of always sending up your most charismatic or persuasive person. If you fail a roll because your stumbled into a conversation, so be it. I don't want to win every roll every time, otherwise what's the point?
