1. You make a good point about the soil Angelika, although it is quite clear that not everyone has access to soil. Or good soil. Urban environments for example.
2. Most lettuces on sale in supermarkets now are hydroponically grown. It appears to be very economical to do so, and hydroponics lends itself to automation. Aquaponics is kind of like organic hydroponics, which has the added advantage of no water changes. While I am not qualified to comment on the quality, my lettuces taste pretty good which is a good sign for me. Granted, I have not compared the same variety of lettuce grown in water and in soil for taste. A New Zealand company is comparing hydroponics with aquaponics:
http://www.berrysmith.org/projects/aquaponics-vs-hydroponics.
3. You could well be correct on the payback time. Although I imagine it depends on scale. No one would invest in hydroponics if the return wasn't worth it. In my case a single lettuce per week (at the cheapest price I can buy it) pays for the electricity, and another lettuce pays for the capital cost. And if I were to rebuild my system I could probably do it for 50% (just what I learned in the process).
4. I have seen photos of a lot of things grown aquaponically. But you are probably right - you cannot grow everything. But you don't need to. If I could pick all of my salad ingredients (except maybe the caesar salad dressing) from my system I would be very happy.
5. The idea of growing fish entices a lot of people. And this probably accounts for the small businesses selling systems. But think about it for a moment. If you were growing fish you would need to get rid of the nutrients. Some people do water changes. Some people grow water lilies. Some people let algae grow. Really smart people create a wetland to soak up the nutrients and recycle the water back into the system. Really, really smart people construct a wetland of lettuces.
Having said all of this, the other posts in this thread make a really good point about the sustainability of using sea-sourced protein to power these systems. It has been noted, by more than one commentator, that the value of these systems are in their vegetable output, not their fish output. So, valuable sea-sourced protein is being converted into the lowest of all uses - growing lettuce. This, in my opinion, is not a good thing.
Some pioneers have experimented with other sources of organic plant nutrient with good success. So it is no longer aquaponics. A common term they use is bio-ponics.
But still, when the electricity stops, so does your food.