Eh, mixed feelings about this. I wouldn't mind it but I would still like to play the game after as a new character. I would hate to lose everything I have. If the play can continue after death then I'm all for it; if not, then forget it.
I'd be annoyed. Every other dragonborn had some legacy and longevity (more or less). It'd just tell me I'm the reject dragonborn, here to basically fulfill some mysterious destiny and die. Not interested.