The discourse around Gojo-centric fics really highlights how split the fandom is on how to handle his power. One major camp treats him like an unstoppable god—fics where he just steamrolls everything, which can be fun for pure power fantasy but gets old fast. Then there's the more interesting strain that explores the vulnerability underneath, the 'Strongest' who's profoundly lonely or burdened by his role. That's where the real meat is, I think.
A huge, huge trope is the 'Gojo needs a break' scenario, which often slides into caretaking or hurt/comfort. Someone—often a reader-insert or an established character like Utahime or Shoko—forces him to actually rest, physically or emotionally. It's a direct response to canon showing him always 'on.' The power-negation or sealing tropes from the manga get repurposed for this; he's depowered, injured, or just finally lets the mask slip, and the dynamic becomes about someone seeing the man, not the legend.
Another massive category is time-travel fix-its, but with a twist for him. He either gets sent back to his youth to prevent Geto's fall (SatoSugu angst forever), or he's the one receiving a future version of his student, leading to a weird mentor/protector role layered with foreknowledge. The dynamics shift from his usual playful authority to something more desperate or determined. And, of course, the 'domestic' fics where he's just a weird, ridiculous boyfriend or parent figure, which play up his chaotic, immature side for fluff. It's a relief from the heavier canon material.
Finally, you can't ignore the crossovers. Because he's arguably the most powerful character in his verse, writers love throwing him into other worlds—Marvel, Harry Potter, MHA—to see how he'd disrupt the power scale. The dynamics become about him being an outside-context problem, either playing a mentor role in a new system or just having fun confusing everyone with his overwhelming strength and personality. It's less about deep character study and more about the spectacle of Gojo unleashed in a new sandbox.