For example, if there was a human or animal genetic pattern that made the organism not age, wouldn't that organism have created many offspring (in its long life) and the mutation have spread?
Does the fact that we don't (appear to) observe any ageless vertebrates or humans mean that it's probably not a genetic problem?
Alternately...is it possible that there are adaptive genetic traits that have not yet evolved, but will evolve in future, or is life on Earth already so old that everything that will exist has likely already evolved?
I think of this as a curve fitting problem: finer granularity of the data points (a shorter lifespan with faster sexual maturation) would more quickly produce a wider variety of genotypes, some of which are more suited to fit to a rapidly changing environment (the curve). On the contrary, rougher granularity of the data (longer lifespan, slower sexual maturation; instead of data points, data line segments trying to fit to the curve) would be more suited to a flatter or gradually shifting curve (a more slowly changing environment).
I think if you have an acute environmental shock, as is happening right now with global warming, the folks who have lots of kids at a younger age will have the genetic advantage from a population perspective (ignoring influences from financial and technological resources).