On one hand -
You wouldn't know who killed who and how many - in a real melee, you might remember a couple of kills because of some strange detail - eg, the naked berserker with dread-locked armpit hair - but most of the time you'd be spearing, hacking, etc rather than checking to see if the last blow had in fact killed anyone. Sure, you would sort of 'know' on an instinctive level, but not to the extent that at the end of the day everybody could sit down and discuss their kills.
Your troops would be in the same boat, especially archers. When twenty bowmen shoot at fifty cavalry, they don't watch their arrows to see who kills and hits what. They string and loose the second, third, fourth (etc) arrow as fast as possible.
On the other -
It would be useful to know exactly who died. It would be realistic if you could go to an NPC, and instruct them: >Hey, Marnid, find out how many men we lost, and how badly wounded the survivors are<
Then, Marnid can trot out a detail of who died, and who is unconscious.
It's also realistic. A commander can't keep track of the losses in a company of 60 or 80 troops - knowing that one haas lost a lot of men is not the same as knowing exactly how many dead or wounded there are. That would have to wait until after the battle.
An additional improvement would be to replace the in-game messages with periodical updates from your senior troops or NPCs, a la:
>Sir! We are winning! There are only a score of the bastards left alive!<
>Sir! We have to pull back! There are barely a dozen of us left alive!<