Should leaders be allowed convert to a religion?

Here's how it would work: If their capital was converted to any religion the leader would convert to that religion, whenever you talk to them you would be able to see their religion and if you shared the some religion they would like you more for it. If war was declared on the "holy city" of their religion they would protect their that city by declaring war.

What do you guys think?

If I understood that right then I'm not sure I would want to declare war on someone just to protect some AI holy city let the AI die. This is assuming I don't have my own holy city but even that can be converted by great prophets.