Nuclear and coal power use in the United States are projected to decline over the coming decades. Here, we explore how simultaneous phase-outs of these energy sources could affect air pollution and distributional health risk with existing grid infrastructure. We develop an energy grid dispatch model to estimate the emissions of CO2, NOx and SO2 from each U.S. electricity generating unit. We couple the emissions from this model with a chemical transport model to calculate impacts on ground-level ozone and fine particulate matter (PM2.5). Our yearlong scenario removing nuclear power results in compensation by coal, gas and oil, leading to increased emissions that impact climate and air quality nationwide. We estimate that changes in PM2.5 and ozone lead to an additional 9,200 yearly mortalities, and that changes in CO2 emissions over that period lead to an order of magnitude higher mortalities throughout the 21st century. Together, air quality and climate impacts incur between \$80.7-\$126.1 billion of annual costs. In a scenario where nuclear and coal power are shut down simultaneously, air quality impacts due to PM2.5 are larger and those due to ozone are smaller, because of more reliance on high emitting gas and oil, and climate impacts are substantially smaller than that of nuclear power shutdowns. With current reliance on non-coal fossil fuels, closures of nuclear and coal plants shift the distribution of health risks, exemplifying the importance of multi-system analysis and unit-level regulations when making energy decisions.