I don’t get that, if you want a legal marriage, then the state has to recognize it and approve of your evidence, what is the huge difference between getting a license from the clerk, or proving to the state that you are married to satisfy them legally?
The state can specify the requirements for a common law marriage and then it is up to the couple to,satisfy those requirements which don’t necessarily include a piece of paper. But if you have a wedding in a church and the statutes don’t prohibit the church from issuing a piece of paper, then that paper could be the functional,equivalent of What we now consider a marriage license. Again, it might take some statutory changes in most states, but I don’t see why it can’t be done. It would probably mean though that more people would blow off getting the paper altogether but they could still claim common law marriage otherwise.