I do agree that debate could be used in all of these ways. But at the same time, I think generality often leads to ambiguity and to papers not describing any such application in detail. And that in turn makes it difficult to critique debate-based approaches. (Both because it is unclear what one is critiquing and because it makes it too easy to accidentally dimiss the critiques using the motte-and-bailey fallacy.)
I do agree that debate could be used in all of these ways. But at the same time, I think generality often leads to ambiguity and to papers not describing any such application in detail. And that in turn makes it difficult to critique debate-based approaches. (Both because it is unclear what one is critiquing and because it makes it too easy to accidentally dimiss the critiques using the motte-and-bailey fallacy.)