My suggestion =Some things in Bannerlord seem somewhat outdated from a design and implementation pov, some of them can be excused but the way reinforcment work cannot. In Bannerlord you often find yourself in a "moving" battle where armies shift back and forth to gain the advantage. However, this back and forth is ALLWAYS ruined when reinforcements spawn out of the air, sometimes almost on top of your units. This is very frustrating and really takes away from what is supposed to be the strongest feature of Mount and Blade, the battles.
The total war games have had a simple solution for this issue for decades now. The reinforcing army spawns outside the map and march into the battlefield where they join the main army. Its very simple but effective because it gives the player time to regroup and reposition the army before further clashes. There might be a better/more interesting solution but this is proven solution to a problem that negativly influence the (arguably) most important feauture in the game.
If you smash the first wave of enemy troops, they, instead of spawning, can retreat from the battle based on some preset conditions.
The main condition for the following triggers should be that the player 'captures' the enemy default spawn zone (by capture, it means that no AI will spawn at the preset location due to player/troop proximity and that:
A) a new spawn location is set (typically the direction of the map border where the AI's party is in relation to the campaign map)
B) the new spawn location hasn't been 'captured/compromised.'
If the new spawn is compromised, the player wins the battle (if all enemy troops are defeated/rout).
The logic behind this is that the enemies can still spawn into the battle, leading to a slightly longer battle, with the AI getting at least 1 reinforcement wave. In this way, the players over-extension can lead to the AI making a comeback in the battle, so long as their spawn isn't compromised. Of course, it would be worth it to find mechanisms to impede the player from taking advantage of poor battle AI (such as holding away from the spawn zone with archers to exploit wave kills)
If the player wins the battle, by removing the AI's ability to spawn/routing them, the triggers that follow in campaign are:
1) Player can capture lord (if its a super-rout), RNG
2) AI can get a retreat head-start by leaving troops (as player can sometimes), RNG
3) A new battle can commence on a slightly different terrain, with the enemy having incurred some morale/disorganization penalties; BUT, player army has a slight numerical disadvantage (to simulate faster troops engaging, with slower troops lagging behind); this can be a temporary debuff (i.e., after 10 minutes of battle, player gets possibility for next reinforcement wave to according to the regular calculations).
4) The player and AI can enter into a parlay (player can let AI go for small relations bonus (0.5 relations maybe).
5) some other interesting options.