I used to feel this way, but looking at how things are going, particularly in regard to climate change, I no longer envy children born today for the world they will live to see. I try to be more optimistic, but that isn't exactly my nature, and events seem to be moving even faster than my pessimism would have predicted.
“The clear awareness of having been born into a losing struggle need not lead one into despair. I do not especially like the idea that one day I shall be tapped on the shoulder and informed, not that the party is over but that it is most assuredly going on—only henceforth in my absence. (It's the second of those thoughts: the edition of the newspaper that will come out on the day after I have gone, that is the more distressing.) Much more horrible, though, would be the announcement that the party was continuing forever, and that I was forbidden to leave. Whether it was a hellishly bad party or a party that was perfectly heavenly in every respect, the moment that it became eternal and compulsory would be the precise moment that it began to pall.”
I can't honestly say whether I find eternal life more appealing than permanent death.
Recently, my two-year-old daughter asked me where she was in a picture of me and her mom. I made the mistake of saying she "didn't exist yet". She seemed horrified by the idea of non-existence. I had never considered before that the eternity of non-existence before birth could be just as horrifying as the eternal death afterwords. I actually find it kind of comforting that death will be no different than before I was born.
Unless you believe in some sort of immortal soul which might blossom into something other than a human consciousness after death, immortality is horrifying. A human mind wasn't evolved to live eternally, and doing so may well be a nightmare. Or maybe we'd just start to forget at some point and hemorrhage past centuries... that would be an extraordinary sadness to me.
But it's definitely true, worrying about death is a privilege granted only to the living.