The essence of a marriage/wedding is the lifetime commitment of a man and woman to each other, for life, for the purpose of begetting and raising children. The lifetime commitment is, logically, primary, since some couples are unable to have children.
Unwillingness to have children, or the inability to perform the marital act, render a wedding/marriage null.
In Christian marriage, grace is conferred. But the priest or minister simply acts as the witness for the Church and the State.
Marriage has a public aspect, as well as a private aspect. Marriage should not be kept secret, for obvious reasons.
Additionally, society has a secondary role to play in the raising of children. It is therefore not unreasonable for the State to register marriages.
Finally, the State must adjudicate custody issues, so it must determine the civil validity of marriages.
You wrote: “Finally, the State must adjudicate custody issues, so it must determine the civil validity of marriages.”
For that reason:
The tradition of common-law marriage was affirmed by the Supreme Court of the United States in Meister v. Moore (96 U.S. 76 (1877))
Because common-law marriages are just as valid as statutory marriages, the Internal Revenue Service does recognize them for federal income tax purposes. Practitioners should be alert to the specific state requirements necessary for their clients contemplating filing joint returns under common-law marriage statutes, as well as those who might be submitting returns as “married, filing separately.”
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Common-Law Marriage
http://www.ncsl.org/issues-research/human-services/common-law-marriage.aspx
To be defined as a common-law marriage within the states that allow it, the two people must: agree that they are married, live together, and present themselves as husband and wife. Common-law marriage is generally a non-ceremonial relationship that requires “a positive mutual agreement, permanent and exclusive of all others, to enter into a marriage relationship, cohabitation sufficient to warrant a fulfillment of necessary relationship of man and wife, and an assumption of marital duties and obligations.” Black’s Law Dictionary 277 (6th ed. 1990).
Before modern domestic relations statutes, couples became married by a variety of means that developed from custom.
These became the elements of a “common-law marriage,” or a marriage that arose through the couple’s conduct, instead of through a ceremony.
In many ways, the theory of common-law marriage is one of estoppel - meaning that couples who have told the world they are married should not be allowed to claim they aren’t when in a dispute between themselves.