Final answer:
Hawaii is considered the most beneficial acquisition during the era of American Imperialism due to its strategic military location, robust sugar industry, and path to full integration as a state, which surpassed Alaska's contributions at that time.
Step-by-step explanation:
During the era of American Imperialism, both Alaska and Hawaii were significant territories acquired by the United States. When evaluating which territory was the most beneficial addition to America, Hawaii arguably played a more prominent role because of its strategic military importance, economic contributions from the sugar industry, and eventual path to statehood that facilitated its integration into the U.S. economic and political infrastructure.
Interestingly, Hawaii was pivotal during major historical events, including World War II, where Pearl Harbor held a key naval base. The annexation of Hawaii also provided the U.S. with a crucial mid-Pacific location for military operations and significantly expanded the reach of American naval power. Furthermore, the sugar industry in Hawaii became a testament to the territory's economic value.
In contrast, Alaska, purchased from Russia, contributed rich natural resources like oil and gold, which have been economically advantageous. However, considering global strategic importance, Hawaii's location and economic prospects during the time of Imperialism made it an especially valuable possession, offering immediate benefits as a way-station to Asian markets and enabling a stronger American presence in the Pacific.