Although marriage licenses issued by the State have been around in Western civilization for about 500 years, ceremonial marriages and common law marriages were predominant. It was an issue of private contract between two parties.
When our country was founded, one could be married by a preacher, enter the marriage in the family Bible, and it would be considered legal. No license required. Many marriages in the Wild West consisted of shacking up together and representing to the public that one was married.
However, in the late 19th Century and throughout the 20th Century, the states started instituting licensing requirements. In the Jim Crow South, requiring a license for interracial marriages was a way to prevent blacks and whites from inter-marrying.
Only about a dozen states even recognize common law marriages today. The licensing issue is all about control. What the state assumes the power to grant, it can attach alot of strings to in the process...particularly on the back -end.
Something to contemplate -- everyday there are dozens of gay ceremonial marriages performed by ordained clergy, though not recognized by the States in which they are performed. By your response, I take it that you're okay with gay marriage.