That caught my interest too since I watched Prison School. I have googled it around in Japanese, but only found that drinking straight from a kettle or a bottle is considered bad manners.
So I've given it a thought myself and that's what came out: if we imagine some dirty and sweaty space far enough from the tap (like on this picture) where people need a lot of drinking water, but no 'luxuries' like cups or jugs - then only a kettle or a plastic bottle comes to mind. And, AFAIK, the Japanese are not the type to keep used bottles. Also, AFAIK, they don't usually drink mineral water, since tap water is safe to drink in Japan, so plastic bottles are only used for soda and sports drinks. And, like that, only a kettle is left for storing large amounts of drinking water. And they drink straight from the kettle because it's too much pain in the ass to pour it into a cup anyway.