The Culture doesn't have quite the same aims as Japan in this scenario. The Culture reluctantly entered into open, large-scale war against the Idirans because they had incompatible morals. The Idirans were religiously-motivated conquerors whose beliefs placed their species above all others, and the Culture is all about personal freedoms. The Culture's goal in the war was to defeat an enemy their ideals could not tolerate and then stop fighting. They were not looking to permanently transition to a more military society, or have those unpleasantly named warships around longer than necessary. The Culture's people knew going into the war that it would be an ugly thing, and the sooner it was done the better.
On the other hand, Japan is not really doing much fighting at all, and their military is even called the "Self-Defense Force." They can't get rid of their military-industrial complex because they already did and what they've got now is what they were left with at the end. It makes sense for Japan to try and make their people comfortable with the idea of coexisting with the SDF, since they will in fact have to coexist with the SDF indefinitely. It's not going anywhere, and it's not really doing anything particularly ugly just sitting there.
On the other hand, Japan is not really doing much fighting at all, and their military is even called the "Self-Defense Force." They can't get rid of their military-industrial complex because they already did and what they've got now is what they were left with at the end. It makes sense for Japan to try and make their people comfortable with the idea of coexisting with the SDF, since they will in fact have to coexist with the SDF indefinitely. It's not going anywhere, and it's not really doing anything particularly ugly just sitting there.