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Cancer is known to be an entirely metabolic disease. Aging, likewise, is a metabolic failure (either implicitly or by natural design ie evolution, for whatever reason). Restoring metabolic function of cells always deages them. Restoring metabolic function of cancer cells always "decancers" them, for instance transplating mitochondria from a cancer cell to a healthy cell or viceversa. Curing aging necessarily cures cancer.
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Aging and cancer have some shared metabolic pathways, but your framing is an extreme oversimplification.

Consider the accumulation of mutation that would occur in a cell not subject to aging.

You could just as easily find support for the counterposition: aging, in a sense, prevents cancer. [0]

0: Judith Campisi, "Senescent cells, tumor suppression, and organismal aging: good citizens, bad neighbors," Cell 120:513–522 (2005). https://pubmed.ncbi.nlm.nih.gov/15734683/

Edit: you edited your comment to talk about mitochondria transplants, but the science I am aware of actually points in the opposite direction: https://pubmed.ncbi.nlm.nih.gov/25565207/

Do you have supporting evidence?

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What do people even mean by "curing cancer", "curing aging", it's not like a single thing in the first place
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Cancer sort of is a single type of thing, which is any mutation that succeeds at uncontrolled division. This can happen as a replication error, or from radiation damage, etc. There are an infinite number of particular mutations that can succeed, and so you get infinite expressions of cancer. But fix the mutations in general, and you fix the cancer.

Aging we don't fully know about yet. Naïvely you would definitely run into cancer problems without it, so that's why I wonder. We'll have to see.

https://news.ycombinator.com/item?id=49832938

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> What do people even mean by "curing cancer"

This one seems pretty obvious. Even the *The Emperor of Maladies manages to bookend it.

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