There are a few things that instantly come to my mind:
1. More immersion through peace time activities. Preferably during "missions" (not on the map). Everyone mentions feasts which are an obvious example, but there could also be things like listening to the petitioners or some interaction with your family.
2. Being able to tell your formation to attack a specific enemy formation (like in the RTS mod).
3. Right now if you're a part of faction/culture X and conquer a settlement from faction Y, you have to recruit troops from their culture. I would prefer either a system that would slowly convert recruitable troops to your culture or making some sort of alternative auxiliary lines.
4. Fix Battanian troop tree:
a) move fians to regular line
b) make their nobles cavalry
c) give more javelins to their skirmishers. they shouldn't have 2 melee weapons as a skirmisher unit.
5. Overhaul the wound/death system. If someone hits 0 hp, give him a very low chance of dying. Then on top of that add some chance based on how much of an overkill was the last hit. It would rightfully kill troops that get hit for 400 hp by an onager and it would allow heavy armoured troops (like nobles) more survivability without making it arbitrary. Heavy armour should make it more likely for you to survive getting knocked out.
6. Overhaul skill progression or companion system. If companions are meant to be expendable, you should be able to find/train engineers etc. faster.
7. If your companion dies, you should be able to retrieve his equipment (perhaps for some price to make up for the cost of fixing it).
Short term:
- reduce that death chance in battles from 10% to 2% already.