Naive question from someone not the least involved in fish farming: why would this assumption fail? Sounds reasonable. Works with humans, too, btw. See skyscrapers.

A open lake is not a controlled environment - unlike a person's house. You cannot change out the water in a lake, it is exposed to all sort of weather and climatic conditions, fauna and flora etc.

The same applies to open farming vs growing something indoors.

Now coming to this example about vertical farming - at much larger scale you will not get the sort of yield/sq.ft you get at a much smaller scale - even in indoor farming.

The vast majority of the energy in the food chain of a body of water comes from the sun so the bigger it becomes, the more volume of water there is relative to the surface area exposed to the sun. You can try to multiple the number of fish by the number of aquariums that would fit into a lake but the vast majority of those fish would starve competing for the limited amount of energy coming hitting the surface.

Thanks for pointing that out. Moving away from skyscrapers you could still successfully scale in 2 dimensions? Which I assume is what fish farming is primarily about, right? Depth brings more limitations like pressure, behavior of gases etc.