It's relatable. We can see ourselves in the normal, everyday situations that the characters are in. For example, if it's a fanfiction about the characters from a fantasy world having to do grocery shopping or deal with a broken-down wagon, it's something we can understand because we've had similar experiences in our own lives.
'Down to earth fanfiction' is appealing because it can humanize the characters. Even if they are from a far - fetched fictional world, when they are shown doing normal things, they become more like us. For example, in a Doctor Who fanfiction, seeing the Doctor having to do things like fix his TARDIS in a more ordinary way, or deal with getting a cold while traveling through time and space, makes him seem more approachable and less of an all - powerful being. This kind of fanfiction can also be a great way to explore the culture and society of the fictional world on a smaller scale, like how the people in a Star Trek fanfiction might have their own local traditions and customs that are only visible in these 'down to earth' stories.