You say that the rebirth is the gift, but the elves are reborn in their children also, which is why their numbers neither dwindle nor grow. Maybe the gift isn't so much the rebirth, but the time of rest. The elves only get this time of rest when they die, which is usually only caused violently and painfully. But the dwarves get this rest from old age.
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"Come away! Let the cowards keep this city!"
-- Fëanor to the Noldor
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