Three reasons to assault a castle:

Assaulting the castle can capture the province for you sooner so you can start using it for income and building etc. as opposed to waiting.

The attack also counts as a win for the commander, assuming of course that you pull it off. I think it's always worthwhile to assault the castle in Shogun before it falls. It can be an easy win.

In Shogun an assault prevents castle down sizing, although I have no idea if this is true in Medieval. If it is that would save time and money in castle improvements.