I would suggest
not to look to historical battles for AI tactics improvements.
- The scale of the average battle in Bannerlord is miniscule compared to actual armies meeting during that period of History
- AI tactics has to work both for 10v10 fights as well as 250v250
- Even at the max troop number, most real cavalry tactics don't make sense in Bannerlord
To expand on number 3, cavalry in bannerlord has 4 roles (in order of importance):
- Fight other cavalry
- Damage enemy morale
- Flank infantry (kind of the same as number 2)
- Mow down routing units
Real world major cavalry uses that make no sense in Bannerlord
- Break enemy lines and create disorganization
- Cut enemy army's from its supply line
- Cut main enemy army from reinforcements
- Cutting enemy units off from retreat to prevent them from regrouping and prolonging the war
- Scouting
- Hit and Run attacks
- Probably a bunch more...
More than any other unit, cavalry needs to prioritise staying in formation above anything else, including dealing damage. Cavalry as a flanking weapon only works as a group, but in Bannerlord the cav formation melts away as soon as there are enemy units within striking range. TW than has to forcebly get these units untangled and reform the formation which takes time and leaves the cav units open to retaliation.
It may be gamey, but each formation should have a primary game role outside of "smack stuff". I don't know why it is so hard to have archer-like units in charge of original skirmish, infantry units in charge of the main combat phase when lines meet (and archers
are no longer able to fire for risk of killing your own units) and cavalry is used to flank or defend against flanking. That is as complicated as it needs to be and it works well for 10v10 battles to 250v250 ones.