Perhaps there shouldn't be a crime for Health, and instead it should be moved to an altogether different feature called disease. Disease has played a huge role in history, and I think you could make a strong argument for it having its own feature.
Disease will be featured. It's another yield produced by some pollution-causing buildings (factories, airports, etc), some resources (tobacco, coal, etc.), and some environments (marshes, fallout, etc.). Probably some other things too that I'm forgetting. If I understand it correctly, the Disease yield counts up toward the outbreak of Plagues.