For me if a population of immortals means a population without children I'm not sure it's such a great idea. I'm concerned about intellectual, cultural and technological ossification and ultimately degeneration without a continually renewing population.
From a moral point of view, I don't buy the idea that death is something horrific to be avoided at all costs. Historically it's generally been accepted that there are things worth dying for, and countless throngs have sacrificed their lives, or at least willingly risked them, for causes they believed in. I'm specifically reminded of the case of a father a few years back that leaped in front of a lorry to push a child to safety, obviously knowing that he was sacrificing his own life to do so.
Human life is precious and valuable, but not infinitely so and it's not obvious to me that an existing life is necessarily more valuable than a potential new one. I don't expect it will be politicaly possible or desirable to suppress life extending treatments and I don't really have any idea how this will all play out, but for me it's not a foregone conclusion that a future in which it is normal to indefinitely extend life is an ideal one.