Roosevelt’s point in his observation about the need to ration his exposure was that Agincourts should be the exception, not the rule. Dwight Eisenhower, who served in the years of the rise of television, used to make the same point. “I keep telling you fellows I don’t like to do this sort of thing,” he told advisers who urged him to go on the air more often. “I can think of nothing more boring, for the American public, than to have to sit in their living rooms for a whole half-hour looking at my face on their television screens.”

Presidents, as John F. Kennedy once observed, are subject to “clamorous counsel” — everyone, it can seem, has thoughts on how they could do the job better. When he was being told what to do and how to do it, Eisenhower — who, beneath his serene surface, had more than a bit of a temper — once replied: “Now, look, I happen to know a little about leadership. I’ve had to work with a lot of nations, for that matter, at odds with each other. And I tell you this: You do not lead by hitting people over the head. Any damn fool can do that, but it’s usually called ‘assault’ — not ‘leadership.’” He went on: “I’ll tell you what leadership is. It’s persuasion, and conciliation, and education, and patience. It’s long, slow, tough work. That’s the only kind of leadership I know, or believe in, or will practice.”

If Mr. Trump is averse to heeding counsel from President Eisenhower — who, as a general with a fondness for businessmen, should be a congenial voice — perhaps he might learn from his own late lawyer. One of Mr. Trump’s mentors from his New York days was Roy Cohn, who as a young man was chief counsel to Senator Joseph R. McCarthy of Wisconsin, whose Communist-hunting from 1950 to 1954 transfixed the nation.

The conventional view of Senator McCarthy’s ultimate fall turns on the Army-McCarthy hearings, when he showed himself to be dark and bullying. The iconic moment came when an opposing lawyer, Joseph N. Welch, asked, brilliantly: “You have done enough. Have you no sense of decency, sir, at long last? Have you left no sense of decency?”

In the popular mind, that question brought McCarthy down. But Cohn believed something deeper was also at work. “Undoubtedly the hearings were a setback,” he recalled in a 1968 memoir about McCarthy. “But there were other more fundamental reasons for his decline. By the time the hearings ended, McCarthy had been the center of the national and world spotlight for three and a half years. He had an urgent universal message, and people, whether they idolized or hated him, listened. Almost everything he said or did was chronicled.”

And that surfeit of attention, Cohn argued, itself contributed to McCarthy’s decline. “Human nature being what it is, any outstanding actor on the stage of public affairs — and especially a holder of high office — cannot remain indefinitely at the center of controversy,” Cohn observed. “The public must eventually lose interest in him and his cause. And Joe McCarthy had nothing to offer but more of the same. The public sought new thrills,” but “the surprise, the drama, were gone.”

To everything, in other words, there is a season, and McCarthy’s hubris hastened the end of his hour upon the stage. “I was fully aware of McCarthy’s faults, which were neither few nor minor,” Cohn said. “He was impatient, overly aggressive, overly dramatic. He acted on impulse. He tended to sensationalize the evidence he had in order to draw attention to the rock-bottom seriousness of the situation. He would neglect to do important homework and consequently would, on occasion, make challengeable statements.”

The urge to overstate, to overdramatize, to dominate the news, was costly. McCarthy, Cohn said, was essentially a salesman. “He was selling the story of America’s peril,” Cohn recalled. “He knew that he could never hope to convince anybody by delivering a dry, general-accounting-office type of presentation. In consequence, he stepped up circumstances a notch or two,” and in so doing he opened himself to attacks that proved fatal. He oversold, and the customers — the public — tired of the pitch, and the pitchman. For Mr. Trump, that’s a New Year’s lesson worth pondering.