I remember the arguments we had as children. "Yes, I am." "No, you're not." Ad infinitum. Maybe it was about whether you were in the top reading group in 4th grade. May be it was about whether you lived in the right neighborhood. What ever.
As a child it was very frustrating to "know" you were right, but to be told confidently by the other (with a smirk perhaps) that you were not. You wanted them to admit they were wrong, that they were only pretending in order to get your goat.
That's the way it is in the Anglican Communion these days. Who is in the Anglican Communion? Some people say they are even though their bishop is not invited to Lambeth. Or they are in the United States but not members of the Episcopal Church. Some people might decide I'm an apostate and say I'm not an Anglican for that reason.
No one can deny anyone their fantasy, or pretended fantasy that they are members of the Anglican Communion. It's not as if we have to swear allegiance the Archbishop of Canterbury or something. Maybe that's a good thing, I don't know.
But what it means is that there's no need for anyone to set up an alternative worldwide Anglican Communion. There's no point. We can all believe there's a man behind the walls of Lambeth who agrees with us. Or even if he comes out and says no he disapproves of you or me, we can ignore him. Whether you're in the Anglican Communion is all in your mind. And when that's so no one can exclude anyone from membership.