One more thought to add to the theory that they are obligate carnivores vs simply carnivores: we sometimes see fish on this forum who are being well cared for but fed a diet of low quality flakes or pellets and their color and activity level is simply terrible. Obviously there could be more to consider there, such as chelated vs non chelated minerals, age of food or exposure to elements, nutrition not being balanced for bettas, or simply being a poor formula, etc, etc. But I still can't help but think that at least part of it might come from a betta simply being unable to digest anything but meat properly or well, and thus grains (rice, wheat, corn, etc) would simply be waste and cause the fish to not get adequate nutrition.
This also means that feeding a high quality food would cause significantly less water pollution by the fish as it would literally poop less.
It also makes me wonder if the cause of bloat so frequently seen could have something to do with either A) the betta being unable to digest the grain filled pellet and/or B) there actually being a bacteria problem like the E. coli we see in cows because they are unable to digest the corn they are fed, thus making them not only gassy, but also literally sick with a bacteria that thrives on the inappropriate diet.
Of course now I am just rambling. Though it makes me really wish I could do some experiments now so I could confirm/disprove any of my above theories. :/
Remember that the tank your fish lives in is his or her's whole world. Ask yourself this question, and answer it honestly: would you choose to live there?