I responded to another commenter, Simpson's Paradox -- 67% average doesn't mean that I can expect 67%. Healthcare efficacy is correlated with wealth (i.e. cost of healthcare and ability to bear that cost). To get 67%, let's say the top 67% of Americans have a survival rate of 100% and the bottom 33% have 0% survival rate. The average is 67%, but I really hope I'm not in the bottom 33% and get cancer.

I don't know what you think a "large fraction of the population" equates to, but in this theoretical, 33% of the population being guaranteed to die isn't exactly ideal.