The problems of the world will always stay the same no matter what generation the world is in ... it's just human nature and it may get better or worse with time. But having the oldest members of our society take control of how to deal with those issues and problems is not a good idea.
And yes, any new technology to lengthen lifespans will first be made available to the ultra wealthy first ... and maybe shared with everyone else later.
And I never enjoy the arguments that people have about population control. Yes I agree that in our current world and current way of doing things ... if we keep adding a few more billion people to the planet, then yes it is very unsustainable. However, if we changed the way we lived and worked and shared all the world's resources, provided education to every person, gave them food, water, medical care and opportunities to live productive lives, then we would have billions of people working towards solutions instead of spending their time maintaining a destructive system in order to survive. Wealth is completely centralized in the world right now to only a few people with the majority of every other human doing their best to just survive ... so their only recourse is to just keep participating in a system that is destroying the planet ... and when you keep adding people at the bottom of that system, it only makes the problem worse.
So the problem is not population size ... its how our world governing system and wealth system works. Because once you feed people, give them comforts, educate them and make their lives livable, then over time, they have fewer children and if done over a couple hundred years, the population would stabilize (and even decrease) to a manageable level. But it would only work if wealth and resources are equally shared and available to everyone everywhere.
And none of these kinds of conversations much matters to someone who is 70 or 80 years of age because they can see their exit and they have no real investment in a future they will never see ... which is why they should not be allowed to stay in power to lead nations.