Church leaders have been political rulers throughout history all over the world. However, I think that they shouldn't be political rulers because they would let their religion get in the way of politics.
A great example of this was during the Tudor Dynasty in England during the 1500's. King Henry VIII decided that because he didn't get a divorce from Katherine of Aragon, he would break away from Rome and become the head of the Church of England, which sparked many rebellions and lots of deaths. Another example is Queen Mary I, she was a Catholic and she decided to burn Protestants for herisy and again, let religion get in the way of politics.