I've been thinking, what about adding level of battle experience as a slight modifier to units' stats in battle? As it stands, there is an "Enemy destroyed" counter that's practically useless other than micromanaging kills for the battle record and for feeling proud of them. So why not turn that stat into a modifier that can affect battle, like slightly increasing damage dealt and slightly decreasing damage taken when in combat. Say in a battle between opposing units of equal numbers and morale on an open field, e.g. both being 10-man divisions at 100% morale with neither being garrisoned in a province; surely one wouldn't really expect to find a unit of recruits being equal in strength to a battle hardened opponent of the same numbers and morale. In that case, battle experience would also be a deciding factor.
Of course, there should probably be a limit on how much battle experience a unit has based on the number of kills it has, but for example, maybe the enemy destroyed cap for experience growth is 3 or 4 times a unit's number then that would also be a cap for the stat modifier in battle, let's say 1.2 times more damage dealt and less damage taken. Of course overwhelming numbers can still overcome it would still be a big difference in close battles. Well, I'll leave the mechanics to the guys in the know.
The point is this then becomes a big deal as managing armies then needs to consider how veteran field units are, so it wouldn't just be a matter of mindless force with numbers. Yes there is strength in numerical superiority, particularly in overwhelming differences, but at least in more balanced match-ups, there would be more strategic thought on which units to field.