Farmed fish also spreads disease and destroys the local ecosystem. Chiles coastline is in pretty bad shape because of extremely large scale salmon farming.
Though I'm struggling to think of even just one example of a human-created ecosystem designed to substitute for a natural one that's been at least as sustainable as those existing in nature.
Sun -> algae -> small fish -> medium fish -> fish we eat.
Very doable, the problem comes in dealing with the waste.
As I understand it, after a few years the floor of the fish farm is basically a solid toxic layer of fish food and fish shit, and it becomes unsuitable for farming. That's not sustainable.
But as things stand right now, the process as implemented is completely unsustainable.