There's this other game that recently started featuring fishing, and at one place it says this about the activity: "You can fish your whole life without understanding it was never the fish you were truly after."

But aside from subjective or personal objectives, there's at least one food recipe which requires specific type of fish (fish 'n' bread, anglerfish). I wouldn't be surprised if they were going to add more fish foods in future, especially if the Ocean biome is going to be in the focus on an update.