Well, let's get the elephant in the room out of the way first: the whole 'Goku x Harem' premise is almost always wildly OOC for him. I mean, canon Goku is famously oblivious to romance, obsessed with fighting and food. That's precisely why these fics have to bend so hard to make it work, and the common themes really show that struggle. There's always a 'What If' catalyst—an accidental wish on the Dragon Balls, a magical artifact, a personality-altering injury—that suddenly makes him aware of women as something other than sparring partners. Once that's done, the appeal is basically power fantasy and wish-fulfillment wrapped in DBZ aesthetics. Readers get to see this ultimate warrior, beloved by everyone, finally 'claiming' the women who've orbited him for years. It taps into that classic shonen trope of the strongest guy getting the girls, but since Toriyama never went there, fanfic writers fill the void.
Another huge theme is 'protection and family' on a massive scale. A harem fic often turns Goku into this patriarch of a super-powered clan, defending his large, expanded family from threats way bigger than what the series usually offers. It merges the DBZ power-scaling battles with domestic fluff, which is a weird but compelling mix. You'll have chapters about Goku building a bigger house on Mount Paozu intercut with him fighting off a new, more dangerous version of Frieza. The appeal there isn't just romance; it's about amplifying Goku's core traits—his strength, his loyalty, his simple-hearted goodness—and applying them to a scenario he'd never conceptualize in the original. It's taking a character who operates on a childlike logic and forcing adult relationships onto him, which creates a tension some readers find fascinating to explore, even if it's mostly just for fun.