Heal death? No, it doesn't 'heal' death. What it does is restart the body's engine after death has occured but while there's a still a window to get things moving again. Buffy and Diana were both clinically (and thus technically and thus according to Science which is the thing Batman does believe in) dead in accordance with prophecy.
When prophecy foretells death, you'll notice it rarely tends to go beyond that actual point unless there's supposed to be predestined eternal damnation/reward or a significant resurrection further down the line.
And I think you're forgetting that Diana comes from a culture that has 3000+ years of propesies actually being right, of direct communication with the gods and fates tied into the Godwave which is by definition above mortal reckoning.
You're also failing to heed the story itself -- when Diana's hit with the bale fire it's made abundently clear that she's the only person capable of not being turned into a cripsy critter by it. Superman would die. J'onn would die. Kyle would die. Arthur would die. Bruce would die. Wally would die.