People focus on the wrong issue so most quotes about evolution are highly misleading: the keyword should be about reproducing. Survival is almost irrelevant. Darwin awards in particular should never be given to anyone with kids (unless they kill their kids too).
"Most grandkids" is good but not catchy.
Or Idiocracy "evolution began to favor those who reproduced the most".
I agree to some extent but I don't think you can really separate the two. You have to survive long enough to reproduce enough. For almost all species, reproduction implies a non trivial amount of survival.
Edit: actually, "almost all species" is not right. Maybe "almost all interesting species"... which is admittedly too subjective a take.