There are some situations that houses inside the kingdom aren't doing their part and that are just occupying bigger cities with less population. Rather than yourselves migrating to another kingdom just to clear their cities making it difficult for yourself to come back if you previously are the bigger kingdom. There should be a way to get rid of them and to provide more space to a bigger house.
Since the majority voted for a King, we are sure to trust that it wasn't done by an inactive party. So, I think it's enough reason to have this kind of power to be able to manage your land for your Kingdom.
Banish could be in a form of city votes sending one's house to another Kingdom or a neutral faction where the house if still active will have to choose a different kingdom in a certain amount of time. And only the King will be allowed to select which specific house/city to banish.
This is to fix inactive houses occupying larger cities and those who are rebellious to the Kingdom and that are abusing the migration system just for their own benefit.