So Bill Clinton appears well on his way back to the White House (albeit in a different capacity) while Kenneth W. Starr, the independent counsel who pursued him and his sexual indiscretions all the way to his impeachment, is out of a job. Anyone who imagined such a reciprocal reversal of fortune belongs in a Hollywood writers’ room — although probably not even “The West Wing” would have offered up such a plot twist.

Mr. Starr resigned two weeks ago from his tenured position as a law professor at Baylor University. He had served the Baptist university as president for six years until May, when the trustees fired him for failing to respond adequately to, of all things, a sex scandal involving assaults and criminal behavior by members of the university’s super-lucrative Big 12 football team. Originally, Mr. Starr, a former federal judge and United States solicitor general, was going to stay on as chancellor. But he resigned from that position on June 1, saying that “the captain goes down with the ship.” Evidently, the original plan to retain his position on the law faculty proved untenable as well.

Just before the story of his imminent dismissal broke, Mr. Starr was taking part in a program at the National Constitution Center in Philadelphia on the subject of the Constitution and the presidency. His comments about his former target were generous, if oblique. He referred to Mr. Clinton’s post-presidency philanthropic career as a “redemptive process” and called him “the most gifted politician of the baby boomer generation.” He added: “There are certain tragic dimensions which we all lament.”

Mr. Starr, named to a federal appeals court by President Ronald Reagan while still in his 30s, was once seen very plausibly as a future Supreme Court justice. Is there a tragic dimension to his trajectory as well? The victims of his coddled football players wouldn’t think so. It seems to me that his story is essentially the story of the corruption that flows from the pact that college administrators make with big-time sports programs. Remember the academic fraud scandals at Binghamton University in New York, so intent on recruiting Division I basketball players that it allowed them to get academic credit for courses like Theories of Softball? Or the University of North Carolina, where passing grades in fake classes enabled athletes to retain their academic eligibility? Mr. Starr took it upon himself to boost Baylor in the football rankings, and he succeeded impressively. The university’s trustees also fired the football coach, Art Briles, whose $4.25 million salary tied him for eighth among his peers — only eighth!

Back when Mr. Starr’s reckless pursuit of President Clinton was driving the country to the brink, I got the idea for a joint biography of the prosecutor and the president. The dramatic appeal of a “shared lives” narrative seemed obvious. Aside from being near-exact age mates (both turned 70 this summer), the two shared a biography of modest beginnings and big ambition, beginning with the magnetic pull that Washington, D.C., exerted on both. From Vernon, Tex., a tiny town near the Oklahoma border where his father was a minister and part-time barber, Mr. Starr found his way to George Washington University, while Mr. Clinton left Hope, Ark. for Georgetown University. And each scored at the very top of the early accomplishment index, Mr. Clinton with a Rhodes Scholarship and Mr. Starr with a clerkship for Chief Justice Warren E. Burger. Both then climbed ever-higher before becoming locked in near-fatal embrace. What a story. What a book.

But a book editor I consulted called it a terrible idea. Clinton haters wouldn’t buy a book that promised to show the president any sympathy, he said, while the president’s supporters wouldn’t buy a book that treated the independent counsel as something other than a twisted Javert.

Years later, Ken Gormley, a law professor and law school dean who is now president of Duquesne University, actually produced a much better version of my abandoned project. His “The Death of American Virtue: Clinton vs. Starr,” published in 2010, is the essential account of the whole episode, aspects of which were so bizarre as to be hard to believe today without the book’s 690 footnotes and its many quotes from on-the-record interviews. A reflective Bill Clinton told Mr. Gormley that “there were some really positive aspects” to the experience. “Once you’ve been publicly humiliated like I was,” he explained, “it doesn’t much matter what people ever say about you again for the rest of your life. And it’s kind of liberating.”

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It’s not only Ken Starr’s downfall that has occasioned this trip down memory lane. Last week, Donald Trump called on the Justice Department to appoint a special prosecutor to investigate whether donors to the Clinton Foundation got special favors from the State Department when Hillary Clinton was secretary of state, an allegation the Clintons have denied and for which evidence is lacking.

Aside from the fact that there is no basis for such an appointment, appointing an independent prosecutor is — unlike my short-lived book proposal — a truly terrible idea. Who said so? Justice Antonin Scalia.

In 1988, well before the Clinton presidency and the Starr investigation, a case challenging the constitutionality of the law governing the appointment of independent counsels, the Ethics in Government Act of 1978, reached the Supreme Court. The law had been passed in response to Watergate. It essentially obligated the attorney general to appoint an independent counsel at the request of Congress, and it took the actual selection out of the hands of the executive branch and placed it with a panel of judges selected by the chief justice.

The dispute underlying the case before the court was small bore — a spat between the House Judiciary Committee and the Justice Department over an investigation of the Environmental Protection Agency’s Superfund program — but the stakes were enormous. The challenge was based on the separation of powers, the argument being that it violated the constitutional structure to have an official who was not accountable to the president performing the quintessentially executive branch function of prosecution.

In Morrison v. Olson the Supreme Court rejected the challenge. Chief Justice William H. Rehnquist wrote the majority opinion. Justice Scalia was the only dissenter. It was a dissenting opinion of which he was deservedly proud, even perhaps his best work. His words were prescient, his analysis airtight.

“Under our system of government, the primary check against prosecutorial abuse is a political one,” Justice Scalia wrote. “The prosecutors who exercise this awesome discretion are selected and can be removed by a president, whom the people have trusted enough to elect. Moreover, when crimes are not investigated and prosecuted fairly, non-selectively, with a reasonable sense of proportion, the president pays the cost in political damage to his administration.”