The event pictured above is probably one of the main reasons why direct military action doesn’t appeal to Japan.
The United States, United Kingdom, and various other close allies (depending on the conflict) direct their focus against terrorism and fight to prevent the spread of weapons of mass destruction. Japan is the only country in the history of the world that has been the target of weapons of mass destruction (twice!). Once untold numbers of your people from two of your major cities have been instantly vaporized as they went about their daily routines, there tends to be a decrease in militaristic fervor.
Since World War II, Japan has definitely been hesitant about taking on direct combat roles, but that’s doesn’t necessarily mean that the country has been on the sidelines while other nations fight a global war on terrorism. Japan has recently contributed to the allied effort in various other ways, particularly when it comes to foreign aid, peacekeeping missions, and continuing to allow a strong U.S. presence at bases in the country.
But all of that is window dressing for the real answer about why Japan isn’t involved in direct combat operations, even when it comes to conflicts in which an allied coalition is formed as an international response: it can’t. Japan’s post-war Constitution (which was basically dictated to them by the United States) prohibits Japan from settling its issues through war. In fact, Japan is technically prohibited from having a standing Army, Navy, or Air Force at all. Japan gets around that prohibition by having an enhanced police force that is capable of responding to internal security threats or providing self-defense, but it doesn’t have traditional branches of military service because it’s not allowed to.