uf haven't found that to be true closed systems degrade the water quality and the condition of the fish. AP is a compromise, finding the point where both plants and animals can find a middle ground. the fish do not purify the water they remove only selected nutrients that they can utilize. trout do their best as do all aquatic animals in pristine water conditions, it's a sliding scale from there.
fish can exist in various levels of nitrate polution, but they are bothered by them as you would be if you lived in a sewer.