The body is suited to dealing with the amount of radiation we normally encounter. Earth shields us from a lot of cosmic radiation and what we see from terrestrial sources isn’t a lot. For radiation to cause real damage it typically needs to damage DNA at multiple spots that are close to each other which makes it difficult to repair. A small amount of radiation is unlikely to do much more than single breaks which the body is able to deal with. Also evolution only cares that we live long enough to reproduce. Through most of human history people would die from disease long before they could get any radiation induced cancers.
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