He changed the selection process for bishops when he was PM so that the PM no longer has a say, even though it was a process that had worked well. I think he thought it would make it more democratic. It didn't. Just the opposite.
I'm no fan of Gordie "where's the vow?" Broon, but I see his logic.
Why should a member of another denomination have any right to choose a leader of the CofE?
After all, the Kirk, in a landmark case, admitted that no-one who is a member of another denomination can be a full member of the CofS.
This excludes the monarch from influencing or interfering in the Kirk, and limits her role to purely ceremonial, when she or her representatives attend the General Assembly and speak, allowing the commissioners to have a ten minute kip.
No-one, of course, is excluded from worship, or partaking of communion (as long as the Kirk Session know of any issue regarding membership of another denomination)