I personally don't prefer anything under 1 gallon for a permanent home and even then I am more inclined to prefer bowls or tanks in the 2.5-5 gallon range.
While with some effort, you can maintain water quality and an even temperature in a .5 gallon bowl, I don't think it's a very humane long-term environment for a betta. I have a 2 gallon cube tank I am using at the moment for some killies and that seems not to offer much in the way of room to move about. I cannot imagine how much space a .5 gallon would offer to a mature betta.
I think sometimes people are way too quick to jump on the "my betta prefers a .5/1 gallon tank/bowl" bandwagon. You have to give fish time to settle into a new environment. Sometimes this can take a couple of weeks. Generally, the more hiding places and areas of cover you offer your fish, the more comfortable and bolder they will be. If they know there is somewhere they can retreat to, fish tend to be much more relaxed than if kept in an empty tank.
While I understand some people prefer to use smaller tanks and bowls, I think sometimes members on here advocate a bit too heavily for their use. In my opinion, this kind of husbandry is no different from someone overstocking a 10 gallon with guppies.
Just because it is possible to maintain excellent water parameters in both these cases, doesn't necessarily mean it is an ideal environment for your fish.
Some members might be offended by what I have posted, but I do think this forum has started to swing the other way in fish care and I see a lot more posts nowadays advocating for the use of smaller aquariums than I did when I first joined.