The Senate still hasn’t voted on ObamaCare reform, U.S. workers are still waiting for tax cuts to drive economic growth and President of the United States Donald Trump is trading insults with the co-hosts of an MSNBC talk show. Yet Mr. Trump appears to be making progress in what might have seemed the most difficult task given to him by voters in 2016: reducing the power of Washington’s permanent bureaucracy.

Secretary of State Rex Tillerson wasn’t exactly dying to move to Washington to run a federal department, but he seems...