The Council holds no authority over any member church. It cannot ordain, cannot discipline, cannot settle a doctrinal dispute, and cannot prevent a member from dividing, merging or leaving. Divisions among Methodist churches are settled by those churches under their own polity, and the Council's membership list simply records the outcome afterwards.
What a consultative body can do is negotiate on behalf of a family that has no other single voice. The Council maintains standing bilateral dialogues with the Catholic Church, with the Anglican Communion, with the Lutheran World Federation, with the Orthodox churches and with the Reformed and Baptist families, and those conversations have produced a long run of agreed statements on ministry, on the eucharist and on authority.
Its most consequential single act outside Methodism came in July 2006 at Seoul, when it associated itself with the Joint Declaration on the Doctrine of Justification, the 1999 agreement between the Lutheran World Federation and the Catholic Church that declared the sixteenth century condemnations on justification no longer applicable to the parties as they now teach. The Methodist association added a third world communion to a two-party agreement, and it was possible only because a body existed that could speak for the family as a whole. That is the argument for having one, and it is more or less the only thing such a body can offer that its members cannot do individually.