Bettas have an aparatus that permits them to breath air. Therefore, you can technically keep them in an aquarium that does not need all of the fancy aeration, filtration, etc. equip.
Bettas also are seasonally in shallow water in the wild. However, they have a TON more space in acres-large rice paddies, even if the water is shallow, than in these cups. Just because they can survive in a puddle during a dry spell doesn't mean they should have to for their entire life.
And finally, once store owners discovered they could survive in small amounts of water, they decided to market fancy eye catching decorative tanks that make them less an animal and more a decoration. And, because people are shallow, cruel, and don't give a flying crap about fish, the fad caught.
In short? There isn't a GOOD reason to keep a betta in a tiny tank. I'm sure that so long as it isn't much more than a foot deep and is well planted, bettas would be fine in a massive tank. They can certainly stress in fast currents, and too much space without enough hiding/resting places, but we have to remember that this is a condition of being bred to have overly large fins. I'm sure wild betta splendens would do just as well in a big tank as any other fish.