Regarding Kol and Elena's love in fanfiction, it can be really fascinating. Fanfiction gives the freedom to writers to explore their relationship without the constraints of the main show's narrative. For example, they could be in a world where the rules of vampirism are different and their love is more accepted. It could also show how Elena, who is often seen in a love triangle in the show, might have a more exclusive and intense relationship with Kol. Writers can play with their emotions, their shared interests (if any are created), and the overall development of their love in a way that wasn't possible in the original series.
In fanfiction, Kol and Elena's love often brings a unique dynamic. It can show Kol's more complex and passionate side. Their relationship might be explored in different settings, like in a modern AU where they meet in a different context than in the show. It allows for creative interpretations of their personalities and how they interact.