There's a significant difference between diffuse radioactivity and the sort of waste nuclear plants put out, though. In both impact on humans, and mitigation.
Well, no - not if the linear no threshold theory of radiation dosages is correct. If it is, then that diffuse radiation leads to cancer just as surely as acute radiation exposure.
Coal wasn't chosen after nuclear was abandoned. Coal was used for centuries before. And the amount of CO2 in the atmosphere is not only from the last 30-40 years. It started to rise significantly with the spreading of the industrial revolution.
https://www.scientificamerican.com/article/coal-ash-is-more-...