People tend to think that [current year] is super late and advanced in the history of the world, and seem to infer from that impression that things that haven't been solved yet are unlikely to be solved. The germ theory of disease is about 150 years old; practical uses for electricity are just over 100; powered flight is just over 100; not using horses as primary transportation is the same; etc. Now is early in the possible history of discovery. There remain hundreds of thousands of important things we don't understand, or even know about, yet.
Besides which, we are talking about a hypothetical future in which we have solved aging; to suppose that future would exist without comparably revolutionary advances in intimately connected biological problems like cancer and dementia is odd.