Your statement makes some unsafe assumptions. Mental state has a strong effect on ability to reproduce and raise offspring. Cancer rarely has an onset early enough to be a factor in this and the traits aren't something that can be "sensed" by potential reproductive partners. Evolution is blind to debilitations that don't impact reproductive ability (this is the same reason our natural healthy lives aren't much longer, on average, than the time it takes for us to be successful grandparents).
Maybe in a few hundred years with a society that stagnated with the exception of a strong stigma being placed on reproduction with people pre-disposed to cancer you'd see a natural reduction in the traits.
Similarly, schizophrenia doesn't usually kick in until your early 20's for males, and early 30's for females, which leaves plenty of time for reproduction, especially in centuries past when we grew up faster.
I found this claim dubious as well. It incorrectly assumes that evolution will cull 'bad' traits and reward 'good' ones. Tell me, what is the evolutionary advantage of the appendix? Fingerprints? The number of human chromosomes?
All we know is that these traits are survivable which says nothing of any advantage or disadvantage they may confer. The author (of the article and this comment) needs to understand evolution better.
"Disposable Soma" theory of aging: in species subject to high levels of predation or death due to other random events, it may be more adaptive to pump energy into reproducing rather than fighting cancer and otherwise maintaining the body.
However, if this were true, wouldn't that mean illnesses like Cancer would also have a survival advantage?