The pH in a lot of those puddles would be so low because of decaying organic matter and rainwater that any ammonia-related toxicity would be minimal because it would consist mostly of ammonium, which is much less harmful.
Unless you can get the pH in your tanks down to 4-6.0, which is what the pH is in a lot of betta habitat, you are eventually going to run into problems with ammonia poisoning unless water changes are not performed regularly. You also run the risk of killing your bettas if the pH suddenly shoots up as any ammonium present will quickly be converted back to ammonia.
My wild bettas although mostly sedentary do enjoy having space to move about. I have no issues with breeders housing their bettas in smaller bodies of water because of the practicalities of their business. The big breeders over in Thailand know exactly what they are doing, and it shows in the quality of the fish they produce.
However, for the casual betta owner with only a couple pet only bettas, there's no really no reason to only provide them with the bare minimum.
While a larger space may not be necessary from a water-quality perspective, I believe fatty liver disease has been linked to the often sedentary lifestyle led by bettas housed in smaller containers. Also I could easily see how muscle atrophy could occur if bettas are not provided with enough room to adequately exercise. This is of particular concern if the betta in question has to cope with excessive or heavy finnage.
Personally, a 1 gallon/4 litre tank is the absolute minimum I would use for permanent accommodation. This to me, provides at least enough room for an adult betta to swim horizontally back and forth.
It is wrong for pet and fish stores to continue to exploit the resilience of bettas, and their ability to survive in less than ideal conditions. Generally the only reason bettas end up in puddles is because the main body of water has dried up, and I wager a high percentage of these die before the next lot of rains arrive. Frankly, I don't really see any reason to mimic the extremes of a betta's environment in the aquarium.