It definetly would be great if auto resolve, at bare minimum, would give same results as F1 F3. Ideally it should first target lowest tier troops before it starts damaging higher tiers. Altough it could sometimes happen, it makes little sense if i loose 3 veterans but no tier 2 infantry. Once i no longer have to change it every single time i open the game, there is no way i would send my best troops in first wave. I might if i can just overpower enemy and suffer no casualties, but besides that i would be far more careful with them.
What I dislike most is that it just doesn't take into account what kind of units you have. It seems to just assign your army a power value and that determines who wins, but it also seems to have some sort of loser bonus where the losing army will often kill twice as many as they have. So 7 bandits end up killing 14 units.
If the majority of your army is made of archers then a few foot soldiers without shields would never even reach them. If the majority of your army is horsemen then enemy archers would get flattened. They should pair up strengths and weaknesses in their calculation.
(Infantry are just bad against everything. They're just a buffer to keep your archers safe. Horse archers are just good against everything because they're so hard to kill and so accurate, but that's a different balance issue.)
Honestly, even if they replaced whatever power level crap they have with a blow for blow calculation it would work far better. With attackers hitting first, since that would make sense.
For example, your rank 6 infantry hits a looter, looter almost dies, a looter hits your rank 6 infantry, your infantry takes very little damage due to armour, then repeat until one dies.
Infantry could have a 20% chance to block melee attacks, upped to 40% if they have a shield. Similarly, if they have a shield their ranged block chance could be set to 80%.
With archers you could make it use ranged attacks vs ranged attacks, or give archers 2 free attacks to account for infantry having to approach and then they play it out like an infantry unit using melee attacks. Archers should also have a basic 20% chance to miss.
For horses it could be that all attacks do double damage, accounting for horse speed bonus (both when attacking and getting hit), but they can't be targeted twice in a row (like, they take the enemy's hit but instead of repeating the round until one dies it rerolls which member of your army is fighting, replacing the horseman, maybe with another horseman specifically to ensure horses take a bit of damage. This would reflect how a charge will take them into and out of range quickly), other than by spear-men (who automatically get the first hit regardless of attacker of defender and negate the double damage bonus and horseman swap after their first hit to a horse). Every hit should have a 50%, or maybe higher, chance to hit their horse instead and if their horse dies the enemy gets 1 free hit on the rider and then they're treated as an infantry unit. They would also have a bonus chance to evade archers, maybe 20%, with up to 40% chance to block if they have a shield. These should be rolled separately so that it can't stack to 100%, though miss chances should be stacked.
For horse archers you could have ranged attack vs ranged attack, like with archers, but with a -40% chance to hit for both sides due to their movement. If we're trying to emulate real battles then just give them infinite attacks against foot soldiers until they run out of ammo since they could skirt and shoot. Otherwise maybe they get 3 hits per enemy hit (though that's still overpowered). Against horsemen they maybe get 1 free ranged attack. Similarly, their horses have a chance to be hit instead and if it dies then the enemy should get a free hit and they should now be considered normal archer units (without the bonus 2 free hits if against infantry).
(Yes this is sorta unbalanced for horse archers... but that's because horse archers are unbalanced...)
Finally, after a unit is killed it should randomly pick the next two combatants from your entire army. This means that you wouldn't necessarily lose high ranking units just because they were picked first and accumulated damage from 10 enemy looters, for example.
That might seem a bit complicated at first glance but any system that accurately reflects your army and gives appropriate results for auto-resolving is going to be a bit complicated.