QUERY is the one missing method to cover all reasonable combinations of safe/idempotent/neither and whether (if safety or idempotency applies) a body needs taken into account to identify a semantically identical request.

Not idempotent: POST

idempotent/not safe: PUT (body matters), DELETE (no body)

safe: QUERY (body matters)/GET (no body)

That’s why QUERY is needed. POST is not a good substitute.