So this book tells us that Gawyn's problem was that he was too proud, that he wanted to accomplish heroic deeds and be a great ruler. It tells us that he needed to learn to stand in someone's shadow.

What?

I'm not sure how to interpret this. The book seems to be suggesting that this was an actual flaw of Gawyn's. That he had to stop behaving like a prince. But that's complete nonsense. Gawyn has to learn to live in someone's shadow? He's spent his entire life in other people's shadow. His entire life was dedicated to being in Elayne's shadow. But more than that, he also spent his entire youth being overshadowed by his half-brother Galad, who was better than him at pretty much everything Gawyn wanted to be. Heck, even after he fell in love with Egwene he stayed in the shadow because he didn't want to interfere with Galad. Although he did command the Younglings and got some notoriety there, notably by killing some of the better Warders, the Younglings themselves were far from an influential force and kept getting the scorn of the Tower Aes Sedai.

What is there to learn? Gawyn was born and raised into a position of subservience, his entire life has shaped him into being a follower. It's hard to believe he actually had difficulty being in Egwene's shadow.

The alternative is that because Gawyn never actually had a chance for any sort of personal glory, he had dreams of doing so one day. Since Egwene will have a lifetime many times exceeding his own (and even if she dies from unnatural causes, Gawyn won't survive her) the Bonding meant that he would have to abandon all his hopes of ever stepping out of the shadows. That makes his character arc pretty tragic, that he had to crush his hopes and dreams so he could have the privilege of serving Egwene. Either way it seemed pretty out of place where everyone else was emerging in glory.