Long before he was president, Donald Trump was a celebrity, a walking, talking jumble of political incorrectness who rode his billionaire populism all the way to the Oval Office.

But a funny thing happened to Mr. Trump once he became president. At some point he understood that if he was not to fizzle out like so many populists before him—think pro wrestler turned governor Jesse “The Body” Ventura in Minnesota or Arnold “The Terminator” Schwarzenegger in California—he would need to tether his populism to the Republican policy...