Agricultural scientists and businessmen are no slouches. If this were truly an economical way to feed lots of people it would probably already be widespread.
Most "high yield" methods you hear about, like raised beds and square foot gardening, basically amount to upping the watering.
I suppose this system really amounts to scrap food recycling. You're feeding the fish various waste organic material that was already grown on a real farm.
The real question is probably: why not just feed it to pigs or goats, the traditional solution? Older folks tell me it was common for there to be residential garbage pickup, separate from trash. The garbage would be taken to farms.
The fish are hungry, that's why not. Aquaponics takes care of the fish waste and plant food, but there is still the question of fish food. Nom nom.
It seems funny to presume that our large-scale food industry is any better at operating in an efficient and economical manner than any other established industry. Computer industry? Up-ended by garage hackers. Music industry? Up-ended by dorm room hackers. It seems reasonable to think that enough people experimenting with agriculture can do the same thing.
If you dig into the Backyard Aquaponics forums, there are plenty of people who are producing more fish and vegetables than they know what to do with, working only in their off hours.