So, because people would watch too many star trek episodes, we should have them die? Doesn't sound too ethical. There is no moral argument for death. As Aubrey de Gray explains, will you ever come to a point where you are perfectly healthy and happy and then decide to just die because the date of your birth was "too" many years ago. I don't think you would decide to do that, even if you had been alive a million years.
Aubrey de Gray's argument is more like - when would you choose to die. You're sitting there, perfectly happy and healthy, your existence has no negative impact on anyone else's. Will you just get up and say - I'll die now, for no apparent reason.
For the record, I'm entirely in favor of serious long-term investment in medical research, and I agree that infinite X (where X is lifespan, health, or any other thing we like) sounds pretty swell.
That said, I'm pretty sure that's the same sort of argument I'm suspicious of. It's not an honest question that "will you"; it's an argument that the answer to that must be no. Not because of any evidence that has been presented, but because you can't think of any answer.
And I think it works because he's assuming an answer to the question he's purportedly asking. We don't really understand what minds are or why bodies age. We don't even understand exactly what happiness is. And he's presuming that a choice like that is possible.
What we do know is that a choice like that is currently unavailable, and I think it's dangerous to build too many sky castles on the assumption that it is.