I can understand why emotions usually wouldn't show up in a fight.  From second to second, a character's focus would be on what was happening rather than what it meant to them personally.  Besides, most veterans would have trained themselves to suppress their fear and uncontrollable anger, since those might hinder them in battle.

That said, you can get some pretty cool moments if you let the personal side of things slip in.  I remember doing one fight where the two characters were hitting on each other during combat.  They flirted, drew closer, and eventually ended up kissing- which one fighter used as a distraction to knee the other in the stomach and then floor them.  The two had another meeting later on, which quickly turned into a violent grudge match fueled by anger over the first fight, and ended up being even more fun than the original.