Isn't it funny how his character kept getting a ton of foreshadowing/potential development (overlooked but awesome brother of Galad, in love with Egwene, portentous Dreams about him, becoming a Warder, getting the bloodrings...) but in the end, he was completely irrelevant to everything, and everyone kinda hated him?
It was a shame. He was treated as a liability, his death meant nothing despite his best efforts and even with three ter'angreal he had a harder time getting to Demandred than the other assassins. Gawyn is one of those characters that just feels like a Plus One, no matter where he is, and his whole line of reasoning for attempting this was in opposition to what he supposedly learned from his character arc of being supportive of Egwene.