One has to wonder what will become of cancer if aging is ever cracked. I really think cancer is the reason life evolved to have age. Because then most cancers can age rapidly and die out early, before they've taken their host with them. We still get cancers, but I would guess we'd get a lot more without age, and not just because we'd live longer.
There are actually multiple forms of cancer that don't reactivate telomerase, and as a result age rapidly and die out on their own. Sometimes these are called pre-cancers, because they could still end up reactivating telomerase before they fully die, and then becoming a full cancer. A lot of them don't however, and a naïve solution to aging would remove this pre-cancer grace period entirely.
Isn’t it the case that the average size of an organism (at least in mammals) correlates a lot with lifespan and cancer rate?
Elephants and whales get cancer much less than humans and humans get it much less than rats. If cancer mutations are a dice roll than the more cells an organism has the more “will I become cancerous” rolls happen, so larger organism had to evolve better mechanisms to kill cancerous cells before they get out of control.
I would guess that smaller animals typically die quickly in the wild, so they don't really face selection pressure against cancers. Larger animals live longer and select for more cancer suppression, including because of their vastly increased number of dice rolls, but also because the longer lifespan leaves more room for cancer over time.
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.
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/
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.
I think you're downplaying the complexity of cancers, viruses are also sort of a single thing, if you don't think too long about it, yet you will never find a single "cure for viruses"
There sort of is a "cure for viruses", actually, but it requires perfectly controlling environment and intake rather than only altering the body, so it's less realistic to live with. Compare replacing unstable RAM sticks to cutting all network access.
This doesn't stop viruses from existing in the first place, though, only from reaching you. If you wanted to stop them from existing in the first place, well, you would indeed have a bit of a hard time. Controlling mutation could theoretically stop cancer from emerging in the first place, if we solve the somewhat less hard problem of altering the whole body (rather than altering the whole planet, as with viruses).
There are actually multiple forms of cancer that don't reactivate telomerase, and as a result age rapidly and die out on their own. Sometimes these are called pre-cancers, because they could still end up reactivating telomerase before they fully die, and then becoming a full cancer. A lot of them don't however, and a naïve solution to aging would remove this pre-cancer grace period entirely.