Cancer and congestive heart failure are both relatively recent, as humans go, and strongly correlated with the Western diet. I wonder what we'd die of if we ate better and still had high-tech medical care.
I read an article once that considered the same question, I think it was something written by Carl Sagan years ago. He ran the numbers from actuarial tables and came to the conclusion that if we could eliminate aging in general and the other major medical reasons for death, we would die from accident with an average life span between 900 and 1000 years.
Of course, that is a lot of other medical problems to take care of first, and living that long would surely create some new ones. And the article pointed out the 900 year figure is contingent upon not just technology but society staying the same, which it surely wouldn't over a period that long.
More to the point, eating better wouldn't solve heart and circulation related problems, just delay the onset of them. A significant part of the reason why cancer and circulation problems have risen to the top of the list is that humans now live long enough to die from them. We need a way to repair damage to return functionality something close to original operational levels.
Jay