Why is there an Arys Oakheart chapter? What do we gain by spending a chapter with him that we could not have gained from another Arianne chapter?
Arys is definitely the least interesting POV, but I think there’s a number of things we gain from being inside his head, however briefly.
1) He contributes to GRRM’s ongoing interrogation of knighthood: how hard it is to live up to your vows, what you do when that becomes clear to you, and how you feel about it and yourself afterwards. The author certainly doesn’t go as deep into these questions with Arys as he does with Jaime, Brienne, Sandor, etc. but that’s part of what makes the soiled knight unique. Arys is neither curious nor introspective, so when his base assumptions are challenged, rather than going on a compelling journey of the self, he falls apart and ultimately commits suicide-by-cop.
2) Indeed, because we’ve been in his head, we understand his decision to charge the poleboat in “The Queenmaker,” lending resonance to his death and weight to Arianne’s self-examination in the aftermath. Half gallant and half stupid, as Arianne says; what would lead someone to think dying this way is their best option? We know, because he was a POV.
3) The structure of the Dornish arc is very precise: from a political panorama of many different actors to an intimate conversation between father and daughter, from a POV whose whole life is stepping back and observing to the POV at the center of it all. The storyline is constantly shedding its skin, engaging in misdirection and carefully withholding information until just the right moment. Arys’ POV is an appropriate step along the way: he provides a window on Arianne’s plans, but he’s an easily manipulated outsider, so we’re still not quite to the core of things.