Variety is not a nutrient.
You can feed a fish all the variety that you want, and still be feeding a diet that is lacking in certain key nutrients, and/or the proper balance of nutrients. At the same time one could feed a single food, made from a 'wide variety' of high quality easily digestible raw ingredients, and never encounter so much as a single health issue in the lifetime of their fish.
Feed a poor quality food, and you'll have poor results. Flowerhorns don't just up & get sick from eating pellets, at least not quality pellets.
The very fact that most fish are opportunists that eat whatever they can get ahold of is a prime example of the amount of dietary plasticity that is found in many wild populations of fish.
I discussed intestinal plasticity in the following past thread on "bloat".
http://www.monsterfishkeepers.com/forums/showthread.php?456034-Bloat-Causes-Cures-and-BIG-Myths
For decades Tropheus keepers felt that due to the intestinal length & long digestive process in that species, it should only be fed low protein "green" food, and that any amount of animal based protein could cause bloat. Yet science has proven that in captive bred species of Tropheus the intestinal length can be half of what's found in wild specimens.
"Intestinal prolongation, although indicative of specialization on diets with low nutritional value, such as those of epilithic algae and detritus, has been shown to be highly plastic (Sturmbauer et al.1992). In Tropheus moorii the intestinal length of domestic fish measured only 50% of the length found in wild individuals (Sturmbauer et al. 1992)."
A more recent study that was published in 2009 demonstrates just how great intestinal plasticity can be in response to the diet quality of various species of fish found in Lake Tanganyika.
http://limnology.wisc.edu/personnel..._Functional-Ecology-LT-cichlid-gut-length.pdf
The above paper clearly demonstrates just how adaptive wild Rift Lake cichlids can be when it comes to their diet. As long as one feeds a quality food, diet will generally be a non issue, and will not cause any type of major gastrointestinal stress. These fish were born to adapt.
A friend of mine spent several months working for the late Stuart Grant on Lake Malawi & one of his daily responsibilities was feeding the thousands of wild caught fish each day. Those wild fish that were all freshly plucked from the the lake were fed bulk commercial flake food, which were mostly comprised of fish meal & starch. Some of these wild fish were also maintained long term on this diet in display tanks. He never saw a single dietary issue in any of the fish while he was there, and that included fish classified as carnivores, omnivores, and strict herbivores. They all ate the exact same food.
I'm certainly not saying that one can't, or shouldn't offer various natural food stuffs as supplements, but it has been proven time & time again that a high quality premium pellet can on its own can keep most species of fish thriving in captivity, not just surviving. Most of the so called natural live/fresh/frozen foods that we offer fish in captivity are nutritionally speaking nothing like what they would encounter and consume in the wild.
Lastly, there are beneficial substances which exist in 'processed' foods, that aren't found in the live foods found in many cichlids natural habitats.
Immune stimulants, growth promoting substances, etc, have been found in a number of feed stuffs of animal origin designed for aquaculture use, such as fish meal, squid meal, garlic, etc. Nutritionists know that these substances are present, but even with today's science some of these substances have yet to even be identified, let alone studied enough to know exactly how they work.
So it's not always as cut & dry as natural or live is better than commercial foods. There's two sides to the coin.