Good timing for this question! Just this week, Zylbrad arranged a private lobby with prox chat via Discord. Pretty hilarious stuff!
Given the very strict chat policies maintained in this game, I can't see it being a good idea. Player bans would be legion. I can't see them adding in more, newer ways for the player base to be toxic to each other. Clearly, Respawn has very different ideas about the parameters of acceptable chat interactions between players than does Infinity Ward.
Heck, they even introduced a mechanic for suggesting alternate ways to gloat, like emoting, when you begin teabagging a player after killing them - even though this causes difficulty for legends who use down on the D-pad for important ability functions.
Brad's video also demonstrates how such a function would facilitate and encourage teaming, as well.