Hey Stevie...great intro to the thread
A true self self sustaining system can also be called an ecosystem, where one's waste is another's food source in equal rates of production and consumption. With the exception of compensating for evaporation, no food/nutrient is added or removed. With typical aquarium systems, there is a constant input (food) and export (physical water removal and/or chemical filtration).
Filtration systems, IMHO, are "life sustaining" equipment that are high flow, high surface area which house bacteria to convert "toxic" fish waste in a two step manner into a relatively non-toxic form. They allow higher "bioloads" for a given volume.
NH3 -> NO2 -> NO3 aka nitrification.
NH3= ammonia
NO2= nitr
ite
NO3= nitr
ate
To expand on this point, if you set-up 2 identical aquariums, one w/a filter and one w/an aerating device. One can keep more fish in the aquarium w/a filter as surface area for bacteria to live on to handle the waste is by far larger than one w/o a filter.
In the process of nitrification, an acid is produced (H+) in the first step as H is "exchanged" for O in the biological process. The buffering capacity/carbonate hardness/alkalinity (kH/alk short form) present in the water is the major component in keeping a stable pH. Once the kH/alk is depleted, the pH will drop easily to a dangerously low level where mostly fish from the Tetra and labyrinth family can survive/thrive.
The end product of nitrification is NO3. The only manner in which it can be removed is by denitrification, water changes and part of the nutrient uptake by plants/algae. High levels of NO3 in the water isn't good for fish longterm. There are more biological processes and other chemical accumulations that occur but the process of nitrification is the main one and will expand from there as need be.
The simplest manner to prevent buffer depletion and NO3 accumulation is by doing regular partial water changes. With all that to take into consideration, is a typical aquarium set-up, in whole or in part, a self sustaining system?