I suspect that this sort of approach may come from imagining "immortality" as a story that you're reading - where's the suspense, the conflict, if there's no real danger? But if you instead imagine it as being your life, except it goes on for a longer time, the question becomes - do you actually enjoy being confronted with mortal danger?

Or, put another way: I'd lay odds that most people would have more fun playing Dungeons and Dragons than Russian Roulette.