These tanks are called " self cleaning ", and to a certain extent, they are - but only to a certain degree.
The fish in the tank will produce waste which is converted into Nitrates which the plants they absorb through the roots.
This is a scaled down version of something called " Aquaphonics " - a variant of " Hydrophonics ", where the fish are used as the source of neutriants for the plants.
However, I would hold reservations about this kind of mixing of 2 very complicated processes ( Fish and Aquaculture ), as the balance between the 2 would be critical to either the life of the fish, or the plants.
Hydroponics is pretty common, at least over here in the states. I'm setting up a hydroponic fishroom. There are many hydroponic farms in appropriate climates.
This is the same basic principle as a Walstad aquarium, so it's actually extremely common all over the world, just perhaps not in this exact manifestation.
I have a silly question (because I do not have any planted tanks); isn't that the same principal as a planted tank where you don't have to do water changes? I remember someone jumping on me once because I suggested a water change, and they yelled at me saying it was a planted tank and you're not supposed to. What about Walstad?
I find this thread interesting, so I'm asking in order to learn.