It's true that there are many age-associated diseases that are morally trivial to oppose: a good society should want to minimize preventable suffering. However, dementia, cancer, and cardiovascular research programs already exist, both privately and publicly funded, and these initiatives have existed for many decades without needing to be labeled "aging" research. So let's be clear and refer to these initiatives as life extension rather than anti-aging, because that is the actual goal.
The best optimist narrative I can come up with is as follows: without the looming fear of death over our heads, humanity will be liberated from (a) the grief of losing loved ones, (b) the suffering of old age, and (c) the capacity lost when someone dies. In particular, (c) might mean that geniuses stay productive forever. A little more fancifully, it is sometimes suggested that the value of a human life approaches infinity as human lifespans approach infinity, so the fear of violent death would effectively prevent all violent conflict.
There is then often an emotional appeal about how much more time we would be afforded for exploring the universe and undergoing personal growth; at this point of the conversation you can really tell that the person trying to sell you on the anti-aging agenda is from California, and has tried LSD (or at least pot), and maybe knows a thing or two about Buddhism and Star Trek. (Perhaps they're even fans of Iain M. Banks?) Just think of all the good someone like the Dalai Lama could do if he could literally meditate for centuries, achieving ultimate enlightenment! What if Terry Pratchett and Douglas Adams never died? How can you afford to say no?!
The answer to this all comes to us from a lesser-known member of the _literati_ of the 20th century, an obscure writer called Charlie Chaplin:
> To those who can hear me, I say - do not despair
> The misery that is now upon us is but the passing of greed - the bitterness of men who fear the way of human progress
> The hate of men will pass, and dictators die, and the power they took from the people will return to the people
> And so long as men die, liberty will never perish
In the optimist's world, where everyone gets to live forever, we do not get to pick and choose who attains that status. Josef Stalin, Fidel Castro, and Francisco Franco all died of old age while actively maintaining regimes that actively harmed their people. On the balance, any one individual can do more harm than good.
...And this is not even discussing the problem of population dynamics—how do we maintain balanced numbers? What kind of work will still need to be done? If people stopped aging suddenly, would there be people trapped in shitty jobs for centuries? (Some of this also applies to mind-uploading.)
If the reaction is, "but surely we can advance robotics to achieve fully-automated luxury gay space communism like Iain M. Banks wanted," then let's do that first, before we let a handful of grossly wealthy private equity goons forge the Rings of Power for themselves. There's no rush, right? Right?