Seeing as two of my choices for this were already done(though for Kirito I'd point out to SAO Abridged too because he gets some great characterization in it), I'm gonna mention the obvious: Tharja and Camilla
Solution: make them not obsess over the Avatar's ****, none of them have a good reason for it.i
The way they were handled were poor, but I'm not against characters who have an obsession. I just think that in order for characters with an obsession to work, they need to develop around why they are obsessed, develop them outside of their obsession and to develop them with their obsession(Not make them more obsessive, but rather, have them and their obsession develop as it goes. As the story progresses, show that obsession turning into an actual respect/friendship/legitimate feeling) That being said:
Tharja: One of the main problems was the fact that her reasoning for being obsessed with Robin was never mentioned outside of a internet-exclusive video. And it's never mentioned after that regardless. Her reasoning for being obsessed with Robin wasn't supposed to make sense, yet it was one of the things that I thought made her interesting. It would've been legitimately cool if they actually explored this bit in the game.
It could've been interesting if Robin actually talked to Tharja about that reasoning and if their supports were about Robin trying to help Tharja to sway away from her dream obsession into an actual friendship between the two. Much like Nohr's poverty issue, it's really sad when they actually give these actual interesting things and yet don't expand on them.
Camilla: Compared to Tharja, who had an interesting reason that wasn't expanded upon, Camilla's backstory and why she dotes on Corrin was revealed with her support with Niles, but besides that, Fates does not have much on backstory/past expansion other than Corrin and Azura. In Camlla's case, she needed more than just a backstory. She needed development. Her character needed to expand out and be more than just a doting guardian to Corrin. Her A-support with Corrin shouldn't have been goofy, but much like the other siblings, something actually heartwarming and developing about her character. She didn't need a bunch of supports with multiple characters with her trying to get them to dot on Corrin.
Like Tharja, she had the tools, but nothing expanded upon them. Her supports with her siblings and other characters like Niles and Odin show her with actual maturity and that she can do more than just doting. Yet her obsession itself isn't really developed in the Supports where it's shown except for Niles and the backstory behind it. Why have Camilla have Silas try to dot on Corrin when you could've had an opportunity to expand both hers and Silas' backstories with Corrin? Despite Tharja's obsession with Robin, she at least had development. We got to see her warm up to other people through her supports, we got to see she wasn't all gloom and doom like in her support with Nowi and we got some decent backstory on her history as a dark mage.