The visits Prime Minister Koizumi made to the Yasukuni Shrine, I believe, had nothing to do with approval ratings. He paid respects at the Yasukuni Shrine to pay respects to the people of Japan who fought and lost their lives for the country and to pray for the peace of their souls.
I think every character actor at some stage likes to carry a film. It can be extremely liberating to just come in for a scene or two and do your thing. But I find it frustrating if I'm just doing little bits here and there for too long.