I didn't read through all of the responses but I would like to weigh in.
It's true that most mechanical filters do not remove large particles, they just trap them. That is why we must clean our filters, removing those particles from the system. If you want a filter that actually removes suspended solids then you should look into a drum filter, which cleans itself.
And yes, clear water is a very hot topic in aquaculture. You have your "clear water guys" and your "green water guys" who disagree on which is best for the fish. As our understanding of the microbial communities in natural environments grows, we are learning that the presence of certain microbes can reduce the levels of pathogens by antagonizing them. This is not limited to the bacteria in the water, but also the communities found on the fish itself (especially slime). Corals have been shown to have hundreds of bacteria species living on them, many of which are beneficial.
Nitrification is of the utmost importance to artificial systems. However, it does leave nitrate as a result. Nitrate IS harmful, but not if the levels are low. How much is harmful depends on the species. In addition to being an endocrine disruptor, nitrate also blocks iodine from being used by the fish. Studies have shown that elevated nitrate can cause goiters that are indistinguishable from those caused by iodine deficiencies. For catsharks a nitrate level of approximately 70ppm has been demonstrated to cause goiters. In freshwater nitrate can be controlled by water changes and sometimes plants (though their ability to do this is often overstated). In saltwater however, water changes are less economical so more often you will see systems designed to have denitrification through bacteria. I wish we saw more of it in freshwater too. However, water changes are still important as they reduce the levels of other toxins and replenish lost minerals.