Would it not be cool if you could initiate dialogue with other players like your character initiates dialogue with NPCs, or like in previous incarnations of the Elder Scrolls.
I.E. My character "Alonzo the Altmer" goes up to your character "Kathy the Khajit" and presses the appropriate button/ command to initiate a dialogue. The other player can accept or decline. If they accept then you are brought face to face with each other (think of a skype video chat, or how you interact with other NPCs). You would be able to have a private conversation, maybe people in the area would be able to overhear in the chatbox in the talk channel, and you could have options to select trade, give, or something else. It would also be fun cause you could probably see people react to the conversation with emotes.
Then imagine if your 4 player group wanted to start a group chat, you know before you enter a dungeon, just to have fun, or to compare and trade loot acquired in PvP or adventuring etc . . . You could initiate a group chat and have the screen split in 4 so you could see everyone and look at loot, watch emotes, trade, recap funny stories of your dungeon run and generally just have a good time.
The feature I am suggesting seems very elder scrolls like and I think it could enhance the game. Imagine groups of players chatting in town or in PvP zones, or other places it seems pretty cool to me.