Final answer:
Foreign governments valued hosting sports events with American athletes due to the events' popularity, the opportunity to showcase diplomatic relations, and the economic and media benefits they provided.
Step-by-step explanation:
Foreign governments were interested in hosting sports events featuring American athletes because these events were major attractions that drew large crowds and significant international attention. They showcased not only the athletic prowess of competitors like Ethel Calderwood and Bobby Rosenfeld, who won Olympic gold medals for Canada, but also served to highlight the cultural and diplomatic ties between nations. Additionally, having American athletes participate could lead to enhanced media coverage and potential economic benefits for the host country due to the influx of visitors and the global prestige associated with hosting successful international sports competitions.