Exactly correct!!! A State Marriage License is the entrance of a contract between a man, a woman, and the State it was issued in. That license exists for the sole purpose of entering into the contract with the State, which then defines what happens according to State Law, when a married couple divorces.
That is ALL a Marriage License is for.
I've long lobbied for the end of "State Marriage Licenses" and for Christians to enter into the Holy Union of Marriage with the blessing of their Priest/Pastor/Deacon presiding over the ceremony and completely skipping getting a State License.
The Church would certainly recognize the marriage as existing, the State on the other hand would not, and the State would be deprived of the "Marriage License" revenues from Christian Heterosexual couples.
There are also income tax implications in this scenario, which I'll skip for the time being.
You are lobbying for something that already exists, and always has in America.
No one requires you to get a marriage license, people do it all the time.