This assumes there are genes that:

a) contribute to age-related mortality, and

b) shutting down helps combat aging.

Can you state which genes these are that do that? Because I don't know of any.

Plus, many genes have pleiotropic effects. There is no specific aging gene.

On top of that, aging is a word that combines to many different factors. For instance, progeria was called accelerated aging. Well, turns out you have a mutation in lamin A. So, it is about cytoskeletal structure that is defect, rather than aging in itself. Of course the effects that this has, looks like an older person then, so it is related to aging. But one can not say it is "accelerated aging" as such. People having a normal lamin A allele still age nonetheless. So the whole term is problematic. And you can find many more such descriptions where xyz is about aging. Well, most of that it is about damage rather than aging. The Hayflick limit, though, is not about damage; that's just that cells fatigue for some reason when their telomeres shorten, but I have not yet read a sound explanations about why that is the case - after all there must be a mechanism in place.