I second this. However, I don't think battle chatter should be text-only. I think it would be best for the battle chatter to be voiced, with a text notification of what ship is saying it. Reason being is that when you're in the heat of combat, taking your eyes away for even a second to read a line or two of text on the edge of the screen could screw you over. With voiced battle chatter, you could hear somebody scream, "We're gettin' our asses kicked over here!" and you know right away that your ships are in trouble.
Alternatively, auditory battle notifications could be easily accomplished without getting voice actors to do a ton of battle chatter. You'd just need to have something like an adviser from any generic RTS game. You know, the person who says "You must construct additional pylons." In Starfarer, he could tell you things like when your forces are under attack, when you or the enemy capture an objective, or maybe when one of your powerful ships is taking critical damage.
Or, an alternative to an alternative, one which requires no voice actors and no money, is the addition of little blips and beeps or other sounds. When a ship of yours comes under attack, you could play a little, non-intrusive beeping noise that accompanies a text message saying "ISS Herpderp is receiving fire," and then you could play a very intrusive beeping noise when you get the message "ISS Herpderp destroyed." You get the idea.