don't know if you have played Viking Conquest Mexxico, in it when you besieged some place there were many immersive options of how to conduct the siege like burning nearby crops, poisoning the well, foraging and the most important encirclement.
Without building encirclement the garrison would make your army's life a living hell conducting guerrilla assaults and grind your guys over time, if you didn't had a strong enough force to stand the assaults it could force you to lift the siege.
Now knowing that and allthough i prefeer the full range of features VC had for sieges i'll keep simple and suggest, what if you had a new siege option for building encirclement after the siege preparation, without it any enemy armies or single lords could pass right through the besiegers and join the garrison without any losses, with the encirclement built they would need to force their way through as it is now and take some loses if they want to join the garrison in defending the walls.
It wouldn't be as deep as the immersive siege options of VC but would give the defenders a better chance, specially if the AI would consider this like: A relief force arrives, no encirclement? good i'll join the garrison / encirclement built? i'll wait outside until our numbers are enough to overwhelm the besiegers like they do right now.
The besieging AI would calculate if they could afford the time to build an encirclement or if would be best to conduct the siege faster and try to storm the walls before any relief force could arrive.
With this i think it would help the players to experience more defensive sieges too, with the current loss numbers (and defensive AI being really bad) it's almost never worth it to break into the besieged settlement to help the garrison, you lose too many good troops for that.
I could not replied this yesterday but biggest problem of this system is :
If we add this encirclement then starting siege assault just after preliminary phase will be best option. Currently it make no sense building additional siege equipments especially for player sieges, even only ladders are enough. If parties can enter settlement then we will force player and AI to make assault as fast as they can.
This can be a good design what you offer but it does not suit current state of Bannerlord. First we must make equipments more important (starting assault with only ladder should result in very hard situation for attackers) and siege mission should be harder for attacker and they need these equipments to be successful.
Other problem is only enterence of settlement is their gate. Then there will be weird situations parties will pass by siegers and enter settlement when there is no encirclement. Player will be disturbed when a party come close his party and we will force him to give up siege and catch him while he is passing by.