You'd probably want something more granular than SOC code and age to identify the difference between the premium licensed professionals earn for having their document and the premium they earn for also being on average more experienced and capable professionals performing more specialised and difficult work than unlicensed ones in their field.
But then the study is far more about headlines than anything else. Disappointed they weren't bold enough to note that the coefficient on "married" was similar in size to the coefficient on "licensed" and use the same dataset to argue that "U.S. Consumers and the Economy Loses Billions to Professionals Being Married"!