So if you lived in a world... in which clinical immortality was an unquestioned human right...ROTFL.
I live in a world where my wife and I had to fight our old insurance company for basic preventive health care. (She tried to have a mammogram in the same year that I had a simple 20-minute physical. Turns out that violated the fine print in our policy, and we had to pay out of pocket.) I'm glad to say that our uninsured, thirtysomething friend just managed to save enough money for his cancer surgery, but others of our friends aren't so lucky. And I live in Massachusetts, where the state has forced insurance companies to sell relatively affordable policies to individual contractors like me. If I lived in a different state, I'd probably be paying over $1000 a month for the privilege of having my claims denied.
So, sure, I'd love for clinical immortality to be possible, and love it even more if it were an "unquestioned human right". But here in the USA I don't even have the "unquestioned right" to effective, existing medical technologies, and that's a more pressing concern.
Meanwhile, would I want to age in a post-Singularity world? Who the hell knows? I don't think you can be immortal and still be recognizably human -- the entire design of humans is predicated on mortality, just as it's predicated on gravity and an oxygen atmosphere and the presence of edible plants and animals. And who knows what the post-human aliens will think?
To the extent that post-singular beings remain human, I think they'll exhibit many of the same self-destructive tendencies that humans do now. I used to be a cancer researcher, and the sight of people lighting cigarettes still makes me angry inside. It feels like they're setting fire to my hard work. But what can you do? To discount the future is part of human nature.
Recommended reading:
On the alienness of the immortal human: William Gibson's Count Zero.
On the psychology of the immortal human: Doctorow's Down and Out in the Magic Kingdom is good. The much shorter, ha-ha-only-serious version is the tale of Wowbagger, the Infinitely Prolonged in Douglas Adams' Life, the Universe, and Everything. (Douglas Adams is one of those guys whose every throwaway joke encapsulates an entire series of philosophical novels.)
On the "unquestioned human right" to immortality: Roger Zelazny's Lord of Light. You may have to read most of it before it becomes clear what I'm talking about, but keep reading. It's an awesome work.