Koizumi has the advantage of:
1) Even if you disagreed with some of his policies, he was cool.
2) He gave good speeches, he was cool.
3) The women swooned over him, he was cool.
4) He balanced internal and external interests - maximizing the number of factions working together, because he was cool.
I hope that was obviously just being a bit silly - but there's a kernel of truth to it. The guy has a charisma factor both domestically and internationally (even if he pissed neighbors off over the annual shrine attendance problem).