“There has to be some sort of license”
Why? Why should you have to pay the government a tax to get married.
To Hell with that.
Because that’s what provides the legal status. For tax filing, joint finances, access to records, etc. I suppose a marriage could take place in a church and the marriage exists to the family and to god. It wouldn’t to the state without some record.
The traditional answer to that is, of course, tradition.
However when Caesar becomes clearly incompetent to oversee marriages, as has been manifest in this case... well, we should not expect competence from the incompetent.