As for revamping the siege process, I'd like it to be more realistic. As Furious and screwtype mentioned, when artillery was used in sieges, they battered the walls continually for months. To represent this, I would make it so that each turn a town is under siege, its walls will take damage, determined by the amount and type of long-range artillery (catapults, trebuchets, cannons, etc.) and the "level" of the walls. This would have no relation to the amount of time it would take for the city to give in due to starvation. It could be shorter or longer. But once the defenses are sufficiently pounded, you could assault the city. In the battle, the walls would be just weak enough that you to still have to use a number of volleys from your siege equipment in real-time (which is just for show, really) to actually knock holes through them.
Good idea, I was thinking of something very similar.
Different types of siege weapons accomplish this with different ways. If you use sappers, the walls will be breached at some locations but the towers are left intact (due to their deeper foundations). If you use cannons or trebuchets (I'm not sure the latter was historicly capable of breaching walls), some towers will be damaged too. If you use a ram, the gates will have been damaged, but your men will take more casualties during the campaign map siege.
Lastly if your stack has a cannon, trebuchet or a catapult, the defenders should take increased casualties. The main purpose of the last two would have been to continuously fire stones or even dead carcasses into the city to demoralise the enemy, afterall.
Siege towers require the least tweaking, they seem reasonably well depicted in RTW.

I'm not well versed in medieval history, so all this is IMHO