It seems that the government licenses were just a tax and record keeping function and that the contractual understanding was the religious vows.
The courts can settle contractual disputes, if they are within their purview.
I wonder, does the first amendment imply that marriage vows are outside the purview of government ?
It is about power. For example, imagine being a black man and a white woman in the Jim Crow South having to apply for a marriage license. By the 1920s, southern courthouses and law enforcement were riddled with KKK members. The licensing requirement was an effective tool to prevent interracial marriages.
I wonder, does the first amendment imply that marriage vows are outside the purview of government?
Doubtful. Speech can be limited by the government. For example, verbally threatening to kill someone isn't going to get that First Amendment protection. I also doubt that the U.S. Supremes would find First Amendment protection for marriage vows in instances of polygamy, bigamy, incest, pedophilia, etc.