Our economic system is incompatible with the next 200 years irregardless of what specifically gets invented.
At 5%/year, that's a factor (not percentage) of 17292 growth; in energy terms that's not quite boiling the oceans, but it is making the poles the only barely livable zone.
In any sense besides energy, this kind of growth implies automation that makes the meaning of work radically different than today. Human or superhuman AI would be an example of that, but the successful creation of that has other complications that we can currently only guess at with less awareness than the Victorians had of climate change or biodiversity loss.
Everyone already dies.
Everything is, before it gets invented. 200 years ago, radio, cars, skyscrapers, anaesthesia, transplants, space travel, plastics, and bioprinting were all scifi. Aluminium was almost exactly 200 years ago.
Voice-to-voice translation and cheap synthetic gem quality diamonds were too, even when I was a kid.
I'm not saying any of this will be easy — from what I've heard, it's sufficiently hard that one would need to do a PhD in the subject just to really understand how hard and I've not done that — but you are made of atoms, and the atoms in your body can be rearranged into a younger form.
That the only mechanism to do so today is called "cannibalism" is an (enormous and repugnant!) implementation detail, even though it's also an existence-proof of the possibility of such a re-arrangement.
Do you know what's not science fiction? People are already experimenting with genetically modifying themselves, because of things as simple as "they don't enjoy lactose intolerance".
> I don’t see what solving aging does to solve any of these problems.
Then you don't understand the actual problems.
Most of the costs we have today from an aging population are that old people are physically weak, get sick a lot, have many expensive complications, and 30 years ago they collectively didn't have enough kids for the next generation to be able to afford to look after them so well.
When you write:
> we can’t deal with the amount of humans we already have at the ages they live to
That's because (1) it's their kids (us) doing the "dealing with", and they didn't have so many; and (2) our natural aging process is awful.
Anti-aging's biggest promise is that it makes age-related degeneration much easier to manage.
(And all that's assuming "you’ll start to see jobs requiring 100+ years experience" isn't obviated by AI).
Do you currently see jobs demanding 50+ years experience?
Even if we ignore the fact that most jobs won't require any more experience to do than they take now just because we live longer, longer periods of time won't seem as costly to us either. Right now 100+ years of experience is absurd because the only way they could ever have that much experienced is if they worked from the day they were born until the day they died, and even then they would need to live an exceptionally long life. If we lived to 200, you could start your career in your 30s, get those 100 years experience, and still have 70 years - an entire current lifetime - to reap the rewards afterwards.
Being more realistic, there is some finite amount of money you need to put away to live indefinitely off interest at any given level of comfort. Right now reaching that threshold in the 50ish healthy adult years we have is a difficult but achievable goal for most people. But with more time you can reach that threshold on a less aggressive trajectory and enjoy retirement for substantially longer (all while being healthier to boot).
As a thought experiment, if you want to imagine how you would feel about your doubled lifespan, consider your current lifespan doubled from some previous threshold. Would you prefer to live only 35 years on average with 50 being advanced old age? Sure there might be some benefits, perhaps some jobs might lessen their experience requirements, but would this be overall a more pleasant world with higher quality of life? We did not choose a 75-100 year lifespan to optimize human happiness, it is just the number we happened to wind up at as a result of a process that did not consider human happiness at all.