I just don't think a story that begins with the mysterious disappearance and later death of a girl, and that repeatedly asks us "What is the life of one boy against a kingdom?" and answers "Everything." would end by answering "What is Lyanna's death against Azor Ahai reborn?" with "Ehh... sad, but true".

I think the many hints to the reader in the text about Lyanna being Jon's mother (that fly in the face of all in-universe evidence!) are an exercise in complicity, to draw readers in and ultimately show them just how easy it is to believe in fairytales like the characters do, and to show the cost of doing so in a way that truly hurts, and makes us think harder about these things. Prophecy has power in ASOIAF, both indirectly because the characters make them come true through mundane acts, and also because there seems to be a magical mechanism that sometimes brings them to fruition in unexpected ways, but this "magic is sort of real" concept is not applicable to reality, and so really isn't very deep– it's just not really worth writing about!

What is applicable to reality is that a sword you get by tempering it in Nissa Nissa's heart is not worth having.