Anti-aging, once developed, will be cheaper than geriatric care: the "ounce of prevention" effect. Governments will be pushing the treatments on people and opt-outs may eventually be denied social services (especially once the knowledge of how to treat advanced pathologies that are now common geriatric conditions fades away).
Very few people want to live to 100000, much less forever. What will produce the very long lifespans is the day-to-day iterated decision, which won't be life vs. death or stay-young vs. get-old, but well vs. sick, where there's an obvious victor: being well. There's the saying, "Everyone wants to go to heaven but no one wants to die." I disagree. Everyone wants to die (at some point in the future, possibly millions of years off) but no one wants to get sick.
Advanced pathology will probably always require human labor to treat (liability, moral issues) and therefore it will always be expensive. Anti-aging treatments will start out expensive but be very cheap within a generation: a $2 pill every month. Technology's pace of change is accelerating, not diminishing.
Aging and dying costs the medical system about $500,000 per person. Then there is the loss of that person's productive potential. Anti-aging treatments are going to be incredibly cheap in comparison to death.
Post-aging population growth is likely to be closer to linear than exponential. Would you really want to deal with 5000 kids for a million years?
There will be a lot of problems with post-aging humanity, but they aren't the ones people propose, especially not the ecological ones. Humanity's ecological load on the planet will max out some time early this millennium. As a cautious transhumanist and a deistic Buddhist, I worry about spiritual emptiness. I think post-aging, post-scarcity might look like the realm of the devas and ashuras in Buddhism (often mistranslated as "gods" and "demigods") which may exist only as metaphor now, but is likely to become reality (for some) in a few hundred years. I see no need and no way to prevent these changes (end of aging and death) and we have no right to do so, but they do run the risk of allowing people to lock themselves into sub-optimal and stagnant states. Also, I may be wrong about the post-aging world and I hope I am. A world with a 50,000-year lifespan may be a spiritual paradise, a pure land. Currently, we have an 80-year lifespan and people only get to use 10-20% of their living time due to economic needs, so we have a world where most people don't develop much at all.
I think none of this will happen, but if it does, another problem I'd forsee is personality decay.
We all accumulate quirks. If you're mauled by a dog, you will understandably be afraid of dogs afterwards. Probably excessively, irrationally so. If you live through a depression, you may become obsessive about saving. If you have a great time polka dancing, you may scoff at electric guitars.
Eventually these things build up to the point where you're a curmudgeon. We say old people are "stuck in their ways." But young people, for all their foolishness, see their parents viewpoints and habits and virtues and prejudices, not with objective eyes - they have their own faults too - but with fresher ones.
If humanity ever consists mostly of people with thousands of years of life experience, accumulated habits, etc - well, that sounds like a pretty miserable existence to me. And maybe a fragile one if larger threats arise. How will you "think outside the box" to respond if you've been building your box for centuries?
Very, very interesting reply. I think that this "personality decay" is a risk worth concern, but I don't think it's as bad as people think it is. Old people become "set in their ways", I think, because with less life to live there is less risk people wish to take with new modes of thought. (Yes, thinking is risky. See: the link between creativity and mental illness, or the fact that substances LSD, despite its physically innocuous nature, can, if used unwisely and with a bit of bad luck, have devastating psychic consequences.)
I don't think this personality decay will be a major problem. When people have nearly infinite life left and all physical manifestations of aging can be held back, I think people will retain all advantages of youth, without the disadvantages after 40 years or so (although behaviors of 100-year-olds in post-aging world may be considered "immature").
Part of why I feel this way is that, as a Buddhist, I don't see much difference between spending (say) 100,000 years in 1200 bodies or in one of them. Impermanence is constant regardless of life span; constantly, thoughts are being born and dying. It's not that different: short lifespans vs. long ones. The current arrangement just shakes us up a lot more. We have 20 years (+/- 15 depending on how terms are defined) of uptime before we are fully formed and spend our last 10 years "unwinding" and not very productive, with this process culminating in a complete loss of physical memory (and complete submission to the force of karma and the will of God-- Buddhism doesn't require belief in God, but I'm a deist) every 80 years or so.
Most changes humanity has made have been slightly positive, but have only enabled and made easier (not guaranteed or enforced) happiness and spiritual progress. In this regard, their improvements to the human condition have been non-negligible but have only increased what is possible, not so much what is realized. I expect post-aging humanity to be similar. Life may become more comfortable without losing all of one's memories (and facing, since no one knows for sure what happens after death, the possibility of nonexistence) every 80-100 years, but it won't become better unless people make spiritual progress, which can't be imposed upon people or "given" through technology. People have to take it up on their own when they are ready. My concern regarding a post-aging and post-scarcity world is that people will just turn into spiritual procrastinators.
Singularity is not going to eradicate death. Aging, yes. That will probably be gone by the mid-22nd century, if not before. Death of the whole brain will always mean what it does today: the end of one's earthly existence. Mind uploading assumes there can be physical control over qualia, and there's absolutely no evidence for that.
In the middle 3rd millennium, aging will be gone and death will be rare (very rare, and exponentially declining so as to make humans post-mortal) but extremely traumatic when it happens. "Breaking News: 134-year-old honors student dies in lunar train crash." 4th-millennium humans will probably store their brains in very safe repositories and control robotic, replaceable bodies through electronic telepathy. Some people alive will probably live to see this, and if I take my next rebirth here, I probably will as well. But I kinda hope not to "make the cut". A hundred years in good health I'd love, but I don't really want to wait around till the heat death of the universe to pass on.
My religious viewpoint, as a deist who believes existence in a higher power to be the most rational belief but denies the existence of "miracles", divine interventionism, prophecy or revealed religion: qualia is a miracle, probably the only one in this world, and the only one we need.
In the middle 3rd millennium, aging will be gone and death will be rare
In several comments here, you use the word "will" a lot. It's possible, but it makes you sound like a crazy prophet. No-one knows for sure how the future will play out.
That will probably be changing soon.