"On that basis, some might object to unqualified, non-elected trade unionists from being granted positions of power"
On the same basis, the unelected 'Captains of Industry' would have no place in the House of Lords, unless you would like to argue that Britain could run purely on the efforts of the bosses, without the workers.   
I often get the impression some people hold the view that working people are a bit of a fluff in the wheels of progress and should have no voice.
As I said, the church fulfils no practical role.
Jim Carroll