Be careful what you wish for, it might just became true.
But in general, you have to ask if the problem that would be solved is bigger than this new potential problem, and do we have the right to make the decision not to develop these therapies and condemn future generation to die from aging? Every day that they are delayed, thousands die.
Maybe hard choices will have to be made: very low birth rates, or some rate of voluntary deaths (religious people who refuse to take the therapies, maybe?), etc. Maybe it'll be no problem because of technological advances (molecular manufacturing, advanced biotech, etc) and we'll have more than enough resources for everybody, and can colonize other planets.
But these problems caused by people not dying so much seem to be smaller than 100k-150k people dying each day after a long-period of suffering and frailty, causing pain to their families and friends. We've cured many diseases and fixed many of humanity's problems so far, and the benefits seem to outweigh the costs. Goal #1 is to cure diseases, living longer is just a side-effect, as it always was.
Objections to curing the diseases of aging must be at least as big as the problem. Otherwise it's the same old thing about overpopulation that has been going around ever since we invented sanitation and vaccines.
Actually the bigger question is what gives you the right to play with mother nature?
> But these problems seem to be smaller than 100k-150k people dying each day after a long-period of suffering and frailty
So? I've had relatives dying, not that big of a deal. They live on in the heritage they leave behind (like their children).
Very low birth-rates so that some old farts with money can live longer?
What do you think, those vaccines or those modern HIV treatments are getting to poor countries like those in Africa?
Nature doesn't care about us (or anything), and our genes don't care about us (only about being replicated). But we care about us, and if we don't take charge, nobody will. Reducing our suffering and making our lives better is a noble goal. It's the same as helping someone on the street or caring for a sick friend, except on a much larger scale.
> So? I've had relatives dying, not that big of a deal. They live on in the heritage they leave behind (like their children).
That's fine, you can refuse to take the medicine, then. But those that want it should be able to develop it.
> Very low birth-rates so that some old farts with money can live longer?
So that everybody who wants to can live longer. Once these things exist, there'll be such popular pressure to make them accessible that it won't be a choice, and like all technologies, at first it will be expensive and won't work very well, and later it will be very cheap and work well. Even if not everybody gets it simultaneously, it's still better if it exists than if it doesn't.
> What do you think, those vaccines or those modern HIV treatments are getting to poor countries like those in Africa?
Would things be better if those vaccines didn't exist at all? And yes, they are getting there (ask the Gates Foundation or Larry Brilliant about his work on smallpox), just not as fast as most people would want to. But that's not the fault of the science.