A betta can survive in a small amount of water but it will thrive in optimum conditions. IMO, It is like being held captive in a prison cell for the rest of your life without doing anything wrong.
Like I said, mine did thrive. They were vibrant, healthy animals. I fed them all kinds of goodies and most hated when I had them held over in my 20 gallon community aquarium while I cleaned their tanks. They didn't like all the noise and commotion!
In the wild, bettas live in still, often stagnated water in hot tropical environments with dirty murky water. That's why wild bettas are generally mostly mud brown... camouflage!! They developed their labrynth organs over thousands of years of living in these murky, dirty, oxygen-deprived waters to cope and thrive in an otherwise harsh environ where larger predatorial fish would otherwise perish. It is this adaptation that made them popular as a fish that doesn't need filtration or aeration. Why? Because they literally DON'T NEED IT.
And as far as space is concerned... again, if you go back to their environment, depending on the season, sometimes they had waters 1-2 feet deep but for most of the year they subsist in low water levels... sometimes in little more than mud. And they are territorial, staking out a small claim of land in their environ and staying there until they are bullied away from it or die. So their life involves them fighting other bettas and swimming around a space that is usually roughly a square foot, but they are indeed happy with less because when kept in bowls, they don't need as much room to hunt for food as it is provided to them.
Goldfish kept in bowls is, most agreeably!, a slow and suffering death by suffocation and poisoning. Bettas are not goldfish, however. They have been kept in small unfiltered containers and bred for battle and beauty for thousands of years without mishap. Instead of being abused, they flourished outside of a natural environment full of run-ins with aggressive neighbors and predators. Some of our newer betta varieties are even becoming more docile and less territorial as they continue to morph into more colorful varieties and shapes (fin-wise). You can't tell me that how I kept my fish was incorrect. I stand firm in that my fish were active, healthy, vibrant, and VERY well cared for.