A lot of other games have done brilliant fishing mini-games -- Torchlight 2 comes to mind, and more recently Stardew Valley; but also a lot of MMOs. Dwarf Fortress also made fishing more interesting* than it is IRL; and I'm pretty sure that there's a Final Fantasy game with interesting fishing options.
Of course, for every great fishing mini-game there's a terrible one too -- Minecraft gets a lot of complaints since its fishing feels pretty tedious.
Fishing really fits with the survival genre though, and that combined with the massive nostalgia of those great fishing mini-games is a strong driving factor of the idea that fishing is something Stonehearth just can't do without.
*Ok, so fishing IRL is a really popular passtime and hobby, and it's certainly not boring. But it's also a long-term hobby, it can take hours to get a nibble and there's no guarantee of a catch. Video game versions of fishing are far from realistic; but they're also designed for quicker gratification; so you spend more time enjoying the thrill of the bite and less time waiting around for it to happen.
But yeah, it's about bringing the game to life and allowing the hearthlings more interaction with their world, as well as adding the familiarity. People who settle next to a body of water will almost certainly end up fishing in it, so it seems inevitable that our hearthlings should do the same.