I don't think that makes sense either because a child with a healthy mother but an unhealthy or dead father will be hugely disadvantaged, especially in paleo times.
I agree that the child's chances would be lowered. But you're forgetting the "selfish gene" - in other words, the germ-plasm of the father is only interested in reproducing itself in the short-term - obviously, if the father survived the illness, other behavioural patterns would kick in and the father would care for the baby.
Another possibility you've overlooked is that many widows turn to other men to help take care of their past children. While a woman with another man's children is generally less desirable to a man than other women, they're still in with a chance.
And then, from a more cynical male perspective, technically the best approach for a man, re spreading his genes, is to initiate multiple romances with women, get them pregnant, and then leave the area to try again with different women, thus greatly increasing the number of children he otherwise would have had. One could argue that "putting all one's eggs(or rather sperm) into 1 basket is not as effective as spreading one's genes all over the place.
