Britain's Queen Camilla and King Charles III, and U.S. President Donald Trump and first lady Melania Trump watch a pass in review from a balcony of the White House during a ceremony in Washington on Tuesday. | Kenny Holston / The New York Times

King Charles III left Washington with the same goodwill from U.S. President Donald Trump that greeted him when he arrived three days earlier as Trump hailed him as "the greatest king,” adding "we need more people like that in our country.”

British Prime Minister Keir Starmer was likely pleased that his gamble of sending the apolitical monarch into the politically charged White House had paid off, but the warmth between the U.S. and U.K. may not last. U.K.…