Curing the diseases of aging might cause problems, but what we must ask ourselves is: Are those problems bigger or smaller than the problems caused by the diseases of aging in the first place?
If your problems aren't worse than 100-150k people dying per day after a prolonged period of frailty and suffering, causing suffering to their families and friends too and costing tons in healthcare, then I'd say it's worth it.
However long you live, you live one day at a time. If you are happy today and in good health, you'll want to live until tomorrow, and so on. But if for some reason you want to stop taking the rejuvenating therapies or throw yourself off a cliff, that's your choice. Let's just not make the choice for everybody else and all future generations by not developing these therapies...
A specific concern I've always had about this idea of indefinite lifespan is that of monoculture. How often have you heard a phrase along the lines of "this is a temporary problem; once the 'old guard' is no longer in charge, society can move forward on issue XYZ"? Make "XYZ" any major social issue we've had in the past thousand years; from fiefdoms to gay rights to democracy.
It's effectively the end of generational cultural change, which might be a good or bad thing, depending on which generation you most identify with.
People still die, from accidents and what have you. In terms of multiples of the average death rate, generational change will be exactly the same. But generations are 10+ times as long in this view.
That's an explanation that rests on group selection, which tends not to be taken very seriously by most biologists. Similarly, group selection explanations of why we age are held only by a handful of researchers in the field of aging.
Most biologists in the field of aging hold that aging is the result of the decreased force of natural selection with age. This is somewhat difficult to explain even with diagrams, but I'll try anyway.
Let's imagine three forms of a gene. One causes you to die at the age of eight, another causes you to die at eighty, and the third never causes you to die. We would expect that the form of the gene that causes you to die at eight would be removed from the population very quickly, since anyone who has it will die before they can reproduce and pass it on. In contrast, the gene that causes you to die at eighty will be rather prevalent, since by that age you'll have already passed on your genes to your progeny. In fact, it will probably exist at about the same frequency as the gene that didn't cause you to die at all.
This is the mutation accumulation theory of aging. Because natural selection acts more strongly early in life, we tend to accumulate genes with mutations that are detrimental later in life. There's also a variant called antagonistic pleiotropy, where you have genes that have a beneficial effect early in life having a negative effect in old age.
"There's also a variant called antagonistic pleiotropy, where you have genes that have a beneficial effect early in life having a negative effect in old age."
That makes a lot of sense. Passing on the genes seems to over-ride a lot of other things, just look at the crazy stuff most (all) creatures do to find and attract a mate.
I remember the very last question is about "what point does getting old has?".
He argues that without aging and dying, populations will stop getting better and will stagnate.
It seemed very appropriate to link here, but I couldn't get a link. Other than a Spanish translation :-(.