There's a couple misconceptions here. Dutch Harbor/Unalaska wasn't invaded — it was bombed, but not invaded. Attu, Agattu and Kiska were invaded by Japan and occupied until a campaign to liberate them the following year. Canadian forces participated, a rare instance of Canadian combat in the Pacific theater of World War II. (The Canadian surrender at Hong Kong is another good example.)

Brian Garfield's The Thousand-Mile War, even though it is now 46 years old, remains the best history of the entire campaign in the Aleutians. As Terrence Cole writes in his forward to the modern printing of the book:

"Though fragments had been published over the years, no one had ever put the whole story of the battle for Alaska together in a comprehensible fashion. In the 1940s, government censorship had stifled news of the war in Alaska, and as a result many Americans had never heard of Dutch Harbor, Adak or Attu. Several embarassing military blunders, including the tragic invasion of Kiska, made some of the top brass of the U.S. armed forces less than eager to publicize their exploits in the North Pacific.

Those who knew about the Aleutian campaign tended to downplay its significance. In his 15-volume history of the U.S. Navy in World War II, historian Samuel Eliot Morison had called the Aleutians the 'Theater of Military Frustration' and claimed that nothing that went on there 'accomplished anything of great importance or had any appreciable effect on the outcome of the war.' According to Morison, servicemen sent to the Aleutians 'regarded an assignment to this region of almost perpetual mist and snow as little better than penal servitude. Both sides would have done well to have left the Aleutians to the Aleuts for the course of the war.'"

By the time the United States reoccupied the Near Islands, it had bomber bases just as close (and with better climate) in the central Pacific. The combat in the Aleutians was brutal but ultimately futile — neither side gained anything by the fighting.