Global human health threats, such as the ongoing COVID-19 pandemic, necessitate coordinated responses at multiple levels. Public health professionals and other experts broadly agree about actions needed to address such threats, but implementation of this advice is stymied by systemic factors such as prejudice, resource deficits, and high inequality. In these cases, crises like epidemics may be viewed as opportunities to spark structural changes that will improve future prevention efforts. However, crises can also weaken governance and reinforce systemic failures. In this paper, we use the concept of the governance treadmill to demonstrate cross-level dynamics that help or hinder the alignment of capacities toward prevention during public health crises. We find that variation in capacities and responses across local, national, and international levels contributes to the complex evolution of global and local health governance. Where capacities are misaligned, effective local prevention of global pandemic impacts tends to be elusive in the short term, and multiple cycles of crisis and response may be required before capacities align toward healthy governance. We demonstrate that this transition requires broader societal adaptation, particularly towards social justice and participatory democracy.