hmmm . . . I've always kind of been on the fence about him. One the one hand, I relate to him a lot for a few reasons. I think he makes a pretty good contrast with Adolin, in a story structure sense, and I think he's a really good character. He does a good job of showing us that all the Alethi nobility aren't the same, from the very beginning of the story. He does have some really good moments too, like when he comforted drunk Dalinor in the OB flashbacks.
But on the other hand, like you said, it seems he never steps up to his problems or has any major character development. I could completely understand how he acted and even the self pitying thing in the first book, but I feel like he hasn't changed at all since then when he had every opportunity and reason to get 'stronger' or maybe more independent. I'm not saying he should change as a person, or loose any of his quirks, that's not right (and I believe he's meant to have Autism, which is super cool on the representation side of things). But I do think he could maybe try and make more decisions for himself. It kind of feels like everyone is dragging him around from place to place, and he never decides to do anything. The lack of character development makes him seem repetitive and boring in the later books, imo.
Perhaps SA5 will fix things, or give him some time to shine.
So . . . I can't really decide if I like him or not. He's certainly an integral part of the story, and I'm glad he's there. I think Brandon could have done more with his character development, but considering how many characters he juggles with this series, it's understandable for someone to get sidelined. I don't think Renarin is a bad character, but he isn't going on my list of favorite characters anytime soon.