Read the post again. It says that perhaps churches should get out of the CIVIL marriage business (i.e., stop acting as agents of the state), but NOT out of administering the SACRAMENT of Marriage.
This already is the case in quite a few other countries, and the Church has lived happily with it. The state has an interest in promoting marriage, regulating divorce, etc., so will not get out of these area. Sacraments are for the Church, however.
So the state will not recognize marriages officiated by the Church, and the Church will not recognize marriages oficiated by the state? It sounds equitable, but in this country the state will use the equal protection clause to compel the Church (and all other entities) to recognize state marriages. In America you gain nothing by this arrangement.