The clergy is not exempt from having government guns aimed at them. They must gain the permission of government to proclaim people married or suffer the consequences.
If you notice, the licence doesn't make you married, the ceremony does, whether it is performed by clergy or government employees who are appointed for that and other purposes.
You might also give some thought to the legal standing of common law marriages.
Government permission doesn't make one married, it allows it. It is totally illegitimate.
An excellent point, thank you for your response. I would be "married" to my wife without a ceremony of any kind. We were just meant to be together.