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