If you recall, Rhaego was supposed to be "The Stallion that mounts the World". And he was never born.
Hence, there is the chance that the "3 heads of the dragon", "Azor Ahai Born Again" are red herrings.
Maybe. Maybe not.
Maybe Jon could have been Azor Ahai born again... until he was killed by the Night's Watch.
Maybe there does need to be 3 heads of the dragon to conquer westeros, meaning that with only 2 targaryens it is not possible.
The concept that a prophesy will come to pass irregardless of the actions of the characters goes against the type of story Martin is writing. A prophesy about a character suggests the character is safe until the prophesy happens. Since no character is safe, no prophesy can be safe from just not happening.
True, but I don't think that makes prophesies powerless, or that they're not worth consideration.
It's not about being safe, it's about the metaphysics of the setting. Rhaego was a perfect example.
Would he have been born with the scales and draconic appearance if not for Mirri's magic? If so, why?
Are prophesies really so fragile that a random sword blow, or treachery, can derail them; or must magic be involved?
And there's always the question of the unreliability of the prophet. Melisandre herself as admitted (to herself at least) that her visions are not always clear, just look a her vision of "Arya Stark" arriving at Castle Black.
Prophesy may not be set in stone, but I don't think you can discount them out of hand without fully understanding what the prophesy meant. Fate can have a way of fulfilling things unexpectedly, for example: If Rhaego's death eventually spurs Dany to conquor the world, is that really different from being the Stallion that Mounts the World?
I don't think any prophesy can be discounted until the tale is done.