"Why define the framework at all?"
because as with all active creative pursuits, the creation of games is a conversation - not just between creators as a literal conversation, but with the medium itself as a more metaphorical one. And when carrying on a conversation, defining your terms is helpful.
imho, the main hinge on which Belonging-games turn is that they center marginalised communities outside of a dominant culture - both thematically and in the playing itself. That matters, and is worth defining - whether you then want to get into the weeds of specific mechanics or not. And it matters because of the underlying history of marginalised communities being, well, marginalised. Making your general design philosophy something that cares about, and values, marginalised communities at the edges of society is important - for the same reason that caring about marginalised communities in other aspects of life is important.
As a general design philosophy, "this game cares about the marginalised" is a good thing to have expressed clearly in the foundation of the thing you're making. It's a statement of intent, and a guiding principle. Compare it, if you will, to the underlying philosophy of art movements: surrealist art was - and is - a broad range of different things in terms of modes of expression (painting, sculpture, writing, etc.), but it is all united in a core philosophy and intent.
Belonging-games - and indeed any other classification of games - works kind of the same way. It's less about the specific mode of expression, and more about your aim and intent as a creator.
And re: PBTA as a classification - aside from it being an IP policy, afaik it is also defined as any game made as a reaction to PBTA in general. Which means that following that logic, even if you make something that is an explicit and intentional rejection of things contained in another PBTA-game.... you're still making a game that fits into the messy family tree of PBTA-games. But it's also entirely up to you if you WANT to define it that way.
.... tabletop rpg cladistics sure are a messy thing to sort out, huh.