Good point on authority. I have not found an answer as to why Christians should, in this age, file civil marriage certificates
Christians should file civil marriage certificates for many reasons. For one thing it is the law and we are bound as Christians to be obedient to civil authorities unless it is against the commandments of God. There is nothing against marriage licenses in the Bible.
1 Let every person be subject to the governing authorities. For there is no authority except from God, and those that exist have been instituted by God. 2 Therefore whoever resists the authorities resists what God has appointed, and those who resist will incur judgment. 3 For rulers are not a terror to good conduct, but to bad. Would you have no fear of the one who is in authority? Then do what is good, and you will receive his approval, 4 for he is God’s servant for your good. But if you do wrong, be afraid, for he does not bear the sword in vain. For he is the servant of God, an avenger who carries out God’s wrath on the wrongdoer. 5 Therefore one must be in subjection, not only to avoid God’s wrath but also for the sake of conscience. 6 For because of this you also pay taxes, for the authorities are ministers of God, attending to this very thing. 7 Pay to all what is owed to them: taxes to whom taxes are owed, revenue to whom revenue is owed, respect to whom respect is owed, honor to whom honor is owed.
Second, it is the God-appointed duty of the civil government to punish evil and approve good, and when done lawfully marriage is a good; about as good as anything on Earth gets. When a marriage is unlawful–such as in a case of bigamy or incest–then the practitioners are duly punished. The churches don’t do that. We may want churches to do that and we may even think they should, but they don’t. They cannot verify to us that Susan and Bob aren’t close relations. They don’t know whether Bob is already married. They cannot even verify that Susan is who she says she is. Nor do they want to.
Some will be tempted to bring up in the comments some failures of civil government such as so-called “homosexual marriage”, or the institution of no-fault divorce. Those are failures, to be sure. The trouble for would-be defenders of the churches is that these points of failure are not points of success for churches. They don’t claim authority over these abominations either. A pastor or priest might mouth something against these sins, but they let them in the doors all the same; even though we are instructed:
5 Therefore be imitators of God, as beloved children. 2 And walk in love, as Christ loved us and gave himself up for us, a fragrant offering and sacrifice to God.
3 But sexual immorality and all impurity or covetousness must not even be named among you, as is proper among saints. 4 Let there be no filthiness nor foolish talk nor crude joking, which are out of place, but instead let there be thanksgiving.5 For you may be sure of this, that everyone who is sexually immoral or impure, or who is covetous (that is, an idolater), has no inheritance in the kingdom of Christ and God. 6 Let no one deceive you with empty words, for because of these things the wrath of God comes upon the sons of disobedience. 7 Therefore do not become partners with them; 8 for at one time you were darkness, but now you are light in the Lord. Walk as children of light 9 (for the fruit of light is found in all that is good and right and true), 10 and try to discern what is pleasing to the Lord. 11 Take no part in the unfruitful works of darkness, but instead expose them. 12 For it is shameful even to speak of the things that they do in secret. 13 But when anything is exposed by the light, it becomes visible, 14 for anything that becomes visible is light. Therefore it says,
“Awake, O sleeper,
and arise from the dead,
and Christ will shine on you.”