Life - Dan Barber said on "Chef's Table" that he felt his produce tasted better and better as he put more life into the soil. The hydro growing medium is relatively sanitized.
Freshness/Ripeness - We had an organic CSA farm box last summer, and in head to head comparisons, the stuff we grew at home (both soil and aqua) tasted way better. I think this is because we picked it when it was ripe and ate it immediately.
I do have some worries about using plastics. unless you are doing a large-scale operation with concrete and / or glass, hydro and aqua both involve water making a lot of contact with plastics. I have to assume that food grade plastics are safe, but no one really knows for sure.
My gut feeling is that as long as you're meeting all the needs of the plant, freshness/ripeness matters more than the presence of other life in the growing medium.
Feed is indeed the big pain point. All good feeds have fish meal and GMO soybeans etc, and the only way to get a reasonable price point is by buying a 50lb bag from a farm supply store. With a 3 month shelf life, you need a lot of fish and a lot of time dedicated to feeding to not have spoilage.
Theoretically a true closed home system could be achieved by routing household urine to a green tank growing algae, solid waste and food waste to a black soldier fly larvae bin, and feeding the algae and larvae to the fish. The BSFL harvest themselves, and the green tank could be periodically pumped into the fish tank on a timer.
None of it would be terribly complicated to build into a new home, but there's no will to do so as most people would find it gross, preferring to eat artificially cheap fossil fuel fertilized products and have their waste magically disappear.
http://www.backyardaquaponics.com/forum is a tremendous resource.