WASHINGTON—President Donald Trump delivered what historians and speechwriters said was one of the most ominous inaugural addresses ever, reinforcing familiar campaign themes of American decline while positioning himself as the protector of the country’s “forgotten men and women.”

In a speech that his predecessors had famously used to inspire Americans to place country before self and urged them to fear only fear itself, Mr. Trump on Friday described the nation as a landscape of “rusted-out factories scattered like tombstones”...