It's important to note that aging is not so much a mechanism to protect against cancer as it is a method to avoid cancer (that is, by dying before cancer develops).
The cell dies or stops working as effectively as before and is potentially replaced by other cells, but the organism lives. So overall, the cell's DNA is more likely to be transmitted.
If the cell lived (selfishly), it could take down the whole organism with it and not reproduce.
I did not know that. Is there a reading on this topic you recommend?