I couldn't find a better place to make this suggestion:

Move the in-game chat to somewhere else than the center of the screen. I also recommend against making it just an optional feature, because people really shouldn't have the chat at the center. Here's why:
  1. People easily get into a dialogue as they see the chat right in the middle of their screens (not a scientific/published finding, just an observation I had while watching some people play).
  2. Center of the screen is too scream-y, hard to ignore.
  3. With only 5-10 chats back and forth, the ice breaks, but the match-made team is still still full of random people with no true empathy for one another.
  4. Points 2 and 3 result in a chaotic and emotional communication.

Now, if the in-game chat was on the left or right, I believe that everything would be different. People, even when flamed at, could just ignore the chat. That's already 1 less player wasting time on flaming (or flame-thinking), and playing its game. Moreover, without the response, flaming person may also get extinguished.

A chat on the side is also conceptually more like a side-talk, which is more suitable for a chat of a team on a mission. Centered-talk is just too centered and is (I guess) the main reason why people feeling like that just HAVE TO get involved in a flame-war.