long story short, is there any possible way we can make flowing water and or air bubbles go over some kind of porous media to grow a colony of bacteria to reliably filter a fish tank that hasn't been done yet?
Much of todays aquarium filtration, did "not" originate in the aquarium field, it comes as an off shoot of the drinking water and waste water industry, simply miniaturized for aquarium use.
I worked at a drinking water facility that used technology from the 1930s that worked great, until it was revamped in the early 90s, to include recent advances in the use of ozone to combat the advances in the discovery of microbiological protozoal pathogens.
Most of the science is not new, and has been around for 100 years or more.
There may be new technologies afoot, for us but may be cost prohibitive.
Around 20 years ago when ozone was becoming prominent in the drinking water field, miniature versions starting popping up for aquariums.
But at a cost of possibly $300 as an sweetening adjunct to the tried and true filtration methods one would still need to use for mechanical and other functions, they seemed not to take off.
There may have also been a safety concern, in the water plant where I worked, we used ozone as a 1st stage disinfectant to oxidize Cryptospodium and Giardia protozoans not killed with Chlorine or Chloramine, but ....any excess ozone not used up in the initial process had to be quenched with an additional system of calcium thiosulfate feeds to prevent the dangers of any excess ozone oxcidizing the human lung tissue of workers. And a series of alarms were installed to warn of any unforscene escape of ozone. You can imagine the cost for the water plant, and in the case of home ozonators for aquaria, the liability to the manufacturer of an ozone surge killing an entire tank of fish, or.....not to mention any lung damage to an aquarist in the room at the same time.
As an aside, I have been using protein skimming (a sort of chemical reaction form of filtration) for over 20 years,
It has been used longer by salt water aquarists, yet has not found favor with more than a few fresh water types.