One of the members here (Dramaqueen I believe?) does keep several of her bettas housed in 1 gallon tanks, but she is a doting betta-mommy, and keeps up on the extra maintenance required to deal with a fish in such a small space.
Smaller space = more work and more risk, so it is not an ideal situation, and not something that is recomended to other members simply because of that. It can be done. It has been done. That doesn't mean it's good.
One gallon tanks/jars are also often used as 'grow out' tanks when raising bette fry for the males of the bunch, as once the reach a certain age they can no longer be housed with another male, sibling or not, and so must have their own tanks - and let's face it, when you have a 100+ betta that each need their own tank, a 2.5 gallon+ tank is not always a feasible option... I don't live in a mansion big enough to house that many tanks of that size, do you? This is only temporary though. Once the males are sold off they generally (hopefully) go to families which will provide them with a larger home.
Other uses for a 1 gallon? Erm, some people use them as quarantine or hospital tanks, which are used to isolate a new betta either when they are just brought home from a store (since let's face it, most store-bought betta are sick) or when a betta falls ill in a tank, especially if it has tank mates, and needs to be isolated. A 1 gallon tank with a bare bottom is much easier to observe a betta in, and to treat with medicine, but hospital and/or quarantine tanks are only temporary and the bettas are then moved to a larger tank once they are clear of infection.
Some peole I hear grow snails in them? I guess that's handy if you want snails... maybe the bettas will eat them when they are small.
1 gallon tanks are often used for various live cultures, like microworms and daphnia, if you want to maybe try supplying your bette with a bit of a fresh food supplement.
Some aquarists also use 1 gallon tanks for just plants. Plants can catch and carry diseaes too, and sometimes it is simpler to propogate certain species in small tanks by themselves until they are large enough and well enough established to be moved to another (larger) tank. Then again, some plant species are just entirely too large for a 1 gallon.