I don't see it as a purely secular thing.

Sure, it can be viewed that way, but there is nothing in the Bible about getting a marriage license (i.e. permission) from the government. There also is nothing about a church ceremony, wedding ring, wedding dress, wedding cake, etc.

All of those things are fine to do, and none are a violation of biblical principles, but those are all optional.

Biblical marriage, if you look at the examples given, is merely (a) agreement to be married, and (b) consumation of that agreement.

It is no different than a typical contract, verbal or written, where an agreement is made, and then a handshake and/or signature symbolizes that the agreement was, in fact, made.

Government has made itself the default contract, when it has no business being that. The "marriage license" was not even a thing until about 100 years ago. The Founding Fathers certainly did not bother with that nonsense.