Been reading fics with that ship since I was a teen, so I've got some thoughts. A lot of writers pick up on how they're both ridiculously smart but in opposite ways; she's like this perfect, polished iceberg and he's just a raw nerve of self-awareness wrapped in a pessimistic shell. That creates constant friction about methodology. She'll want to solve problems elegantly, through structure and logic, while he'll bulldoze through with brutal honesty and self-sacrifice, which she interprets as needless martyrdom.
Their fundamental conflict isn't about liking each other, it's about understanding. He thinks she looks down on him, she thinks he doesn't value himself enough to accept help. It makes for great slow-burn where progress isn't just confessing feelings, but actually learning to communicate without their defense mechanisms. My favorite fics are the ones where they're forced to work together on a project after the Service Club ends, and all their old habits just don't work anymore. You see them floundering, trying to navigate a real relationship with the same tools they used for fake politeness, and it's beautifully awkward.
Honestly, the best tension comes from moments where Yukino tries to be kind in her super reserved way and Hachiman totally misreads it as pity, shutting down. It hurts so good.