The state is involved in marriage licensing for 2 reasons. First, it was established to prevent interracial marriage. Second, it is a source of revenue both before and after the marriage. Divorce is a substantial revenue generator for the state.
There is no legitimate reason for churches to accede to the state’s involvement in the sacrament of marriage. It is a rite of the church, like baptism or communion and is a commitment between a man and a woman committing their marriage to God. Perhaps this is why many couples are living together without a license.
And of course inheritance and spousal rights have absolutely no consideration in this theoretical secular construction of yours.