Since I consider confucianism a religion, I voted that this was a bad idea.. beyond that, I don't agree with the dynamics you have suggested in general
I always liked the idea of each civ being able to found a religion (named upon founding) through some act, and changing the way they work for the most part.. to me it seems the way they are, it rubs me uncomfortably.. but thats not the best solution anyways.. I have been considering this with great detail lately, looking through game files and such