It's been awhile since I've had geometry class, but three geometric terms (are they all conic sections? I don't remember) come to mind when arguing for an actual wedding ceremony. And all three describe and establish relationships that foster commitment to marriage.
The first is a horizontal line connecting the couple--the bride and groom being the normative couple but it's equally applicable to same sex unions. The couple are joined by a line when they recite their values. The line goes in both directions equally. Mutual submission. Mutual commitment to the relationship. Etc. This is the line established with "I do." It is a covenant between two people.
There is also a plane of commitment, though. The couple stands at the center of an ever-increasing circle, developing relationships with all the family and friends present. The couple gives away their commitment to this relationship through trust to all those gathered. The gathered likewise share in this social covenant that they will support the new couple through advice, prayers, leading by example, etc. A common part of many wedding ceremonies points this out with words along the lines of "let all those already married be renewed in their vows" etc. The circle is ever growing because this web of relationships is ever growing. The couple also owes a vow to any children that result from the marriage, any nieces, nephews, friends' children, etc. The greater the social web, the stronger the marriage bond for all involved.
Lastly, there is a vertical line between the couple and God (or whatever transcendent reality you'd prefer). This line also goes both ways, but is not equal.
Wedding vows that take place solely on the horizontal line through some sort of legal document are not doomed, but they have less resources to call on in times of stress. A wedding whose vows take place between a couple, between a couple and their friends/family, and between a couple and God have much greater resources, in both strength and number, to call on in time of need.