There have been loads of answers, and many people are still parroting the same propaganda spread by money-minded manufacturers & retailers of goldfish bowls & other small 'tanks'. It's one of the most insidious & dangerously pervasive misinformation that has plagued this hobby for eons.
Theoretically the fish can certainly live but the real follow-up question is "for how long?". I fail to see any benefit in aiming to keep fish alive for only a very short time. NO fish can survive long, grow well & thrive in a small, unfiltered tank. This also includes bettas who, contrary to popular misconception, do not live in "small bodies of water" in their country of origin. I would hardly call rice paddies that are constantly at least semi-flooded (way bigger than your house's total floor area), river streams & long canals "small bodies of water", right?
Constant gulping of air at the surface is NOT normal, this is a condition called hypoxia or oxygen deprivation. Which only proves that bowls & other small containers can support only a very limited amount of oxygen in the water, which is further worsened by lack of some kind of aeration. Goldfish are coldwater fish who need way more oxygen than tropical freshwater fish, so it is even worse to keep goldfish in such conditions.
The smaller the tank, the faster the water quality deteriorates from the fish's urine, poop and decayed uneaten food. So actually larger tanks are definitely easier to maintain & are more stable. The aim should be to have better water quality & need for less frequent water changes, so people who want smaller tanks that are also unfiltered are only making things difficult for themselves. If keeping goldfish, they are champion poopers which makes a good filter even more essential.
As for tap water, it varies widely even within the same country. So one person's success with water straight from the tap is quite unlikely to be duplicated by someone even in the next city. The safest is still to use a water conditioner that can deactivate both chlorine & chloramine, as well as removing heavy metals. Best also to wait about 10 mins after adding it before using the treated water in your tank, to give it time to thoroughly treat your water.
Common goldfish & Comets can reach a max size of 1 foot or 30cm, with fancy goldfish half that size, hence are commonly kept in outdoor ponds. Indoors, they need at least a 3 foot long tank. They can live for decades in the right conditions & practically become lifelong pets that children grow up with. However, they will never live to die from old age as long as misguided people continue to stress them out in wildly inappropriate living conditions.