The dynamic between Kirito and Eugeo is so often about exploring forms of devotion that can't exist in the real world, and fanfiction latches onto that. A huge theme I see is sacrifice, but not the big dramatic kind—it's the quiet, daily sacrifice of one person's autonomy or peace for the other's well-being. There's a ton of hurt/comfort where one of them is recovering from the Axiom Church trauma, and the other is just patiently there, not pushing. It's less about romance and more about this profound, aching loyalty.
Another common thread is rewriting their ending, of course. But what's interesting is how many fics use the Underworld's time-dilation as a metaphor. They'll have one of them outlive the other by centuries in the real world, or get stuck in a frozen moment together, grappling with eternity. The emotional core is usually this bittersweet, doomed feeling, even in fluffy AUs, because their canon fate casts such a long shadow.