I don't know if this is the only reason, but I'm going to bet this is mostly due to the strong family ties between prime ministers, either through blood or marriage. If you look at the list of Christian prime ministers in wikipedia you will find that, out of the three catholic ones, Shigeru Yoshida and Taro Aso are grandfather and grandson, as are the protestant Ichiro Hatoyama and Yukio Hatoyama. I don't have time now to look into the relations between the others, but I wouldn't be surprised if they had similar connections.