It’s not about Jaime’s arc, it’s about hers.
All Brienne has wanted for some time is to live up to the highest ideals of true knighthood, by selflessly giving her life to save her charge, just like Aemon Dragonknight, etc. Twice she has failed (Renly, Catelyn) for reasons entirely outside of her control, so following the third, she will go down swinging heroically in a judicial duel witnessed by the gods.
As with Syrio Forel, that’s her version of a beautiful death.
How does this vision of the end of Brienne work in tandem with Jaime’s weirwood dream though – with the two of them with magical swords fighting against an icy Rhaegar and company?
I mean – your idea is one way for Brienne’s story to end, but so often I see Jaime’s weirwood dream ignored in analyses of what’s going to happen next.
How is it inconsistent with it? LSH is the literal embodiment of the vengeful dead, Brienne’s got the magic sword, and I imagine Jaime will fight as best he can to save his own life…but unlike in his dream, Jaime is still missing his sword hand and hasn’t trained himself back to normal, likely requiring some saving.