Curing cellular aging would not, as far as I know, have any effect on cancer. Whether it would have any effect on other problems like decreasing bone density, I'm not sure. So even if you sweep one cause of death completely off the table, it stands to reason that whatever you would have died from next will still be around to do the job until it, too, is cured.
Much like when you add more of the limiting reagent to a chemical reaction, it just means that some other reagent will now be the limiting reagent.
Much like when you add more of the limiting reagent to a chemical reaction, it just means that some other reagent will now be the limiting reagent.