The constant and most grating tension usually comes from the pile of female characters orbiting Kirito, each with unresolved feelings while the guy remains, for the most part, oblivious or passive. You see Asuna as the canonical partner, but then you've got Lisbeth, Silica, Sinon, Leafa, and sometimes even Alice all in the mix. The primary conflict isn't really about fighting monsters; it's about navigating this emotional minefield without blowing up the established 'Kirisuna' endgame that so many readers expect.
A lot of stories try to resolve this by making it an actual harem ending, where everyone somehow agrees to share, but that often feels forced and requires bending characters out of shape. The more interesting ones, to me, are where the conflict shifts inward—Kirito grappling with guilt over leading people on, or one of the other girls, like Sinon, making a conscious choice to step back and prioritize friendship. Those moments feel more true to the characters than just adding more bedrooms to the cabin in Aincrad.
The real trick these fics pull is keeping the action stakes high enough that the romantic tension doesn't become the only plot. If it's just girls blushing at Kirito for 20 chapters, I'm out. The good ones weave the personal conflicts into a new game threat or a guild crisis, so the relationships develop under pressure.