The American taxpayer does something different than you state. In actuality, they fund the projection of force everywhere that the US has interests. To relate back to the example of Japan, this means that the American taxpayer funds the defense of the things the US wants from Japan, not truly the defense of Japan itself though the defense of the former can often aid the defense of the latter. This holds true essentially everywhere else the US chooses to project force and the distinction is absolutely critical but too easily forgotten.
EDIT: in case the above sounds a bit too much like some kind of anti-American rant, the point I should have made more explicit in response to the parent is this: parent makes it sound like Japan is restricted from defending itself against the listed neighbour countries and therefore requires outsiders to do so. This is not true, and since it is not true, one should periodically ask themselves why the US has forces there (and everywhere else.)
http://www.japantoday.com/category/commentary/view/japan-bal...
Because the Japanese were forced to include in their post-WW2 constitution that they would no longer have a military for any purpose other than self-defense. As a result, the American taxpayer pays for the US military to be stationed in Japan for the purpose of offensive attacks against threats like North Korea, Russia, and China, thus indirectly also funding Japan's self-defense. This means Japan's self-defense expenses also drop, not to mention any offensive attacks (as long as the US agrees with them, which it probably would) come free of charge to the Japanese.