It would be cool, but it would require more data to be stored, we don't know if they are storing that data. Also consider that it's not as clear cut as you seem to think, an example would be... you take 90% of a pokemon's HP with an attacker, then switch or it dies and finish it up with a different attacker, does it count as a win for the second one, and a loss for the first?
GamePress
An idea: battle stats
It would be nice to have battle stats for each single Pokemon you own. Something like the number of battles fought and battles won (how many pokemon it beat) on both attack and defense.
It would allow a more "personal" connection between trainer and pokemon, something that PoGo really lacks compared to other games - your Charizard would feel more unique, and you'd at least get some kind of reward for using him.
Also, keeping great stats on your favourite mons could be a bit of an extra challenge and a "reward" for the good players. And I'm not a coding expert, but I suppose it would be quite easy to implement!
What do you think?