That actually was a serious concern, both to the US and to the Japanese government itself. If the Emperor and the military leaders had been killed, there was no one who could legitimately order the remaining military to surrender. And the Japanese Army was not small at the end of the war (https://www.nationalww2museum.org/war/articles/there-are-no-...). In addition to the military in Japan (900,000 on Kyushu to oppose US landings), there were something like 1,500,000 in China, Burma, and Southeast Asia.

The result could have been "warlord" led militaries seeking to establish their own territories and fighting with others. Not unlike Afghanistan or China in the 1920s and 1930s, or some other failed states around the world.