The event comes with a captive audience of thousands — Republicans, Democrats, “apolitical” relatives, little siblings too young to vote. Everybody sits trapped in their bleacher seats. After 20 minutes, they dutifully applaud.

For a politician, a commencement speaking gig offers the kind of advertising that money can’t buy. “You have people of all different backgrounds gathered,” said Senator Cory Booker, a Democrat from New Jersey, who delivered two dozen virtual commencement speeches this spring. “It’s a time of extraordinary diversity.”

Mr. Booker recalled that when he was chosen to give the address at the University of Pennsylvania in 2017, there were Republican trustees “pooh-poohing” the choice of such a partisan speaker. (He won them over, he said, with his focus on “our common values” and “the larger body politic.”)

College graduation ceremonies are fittingly focused on the graduates, but for some 20-odd minutes the spotlight turns to the illustrious speaker. Ideally the audience, in what Mr. Booker called its “extraordinary diversity,” might inspire a speech that transcends ideological divisions, as some of the most memorable ones have. The Apple founder Steve Jobs earned his spot in the commencement hall of fame with a 2005 speech at Stanford University reminding students that “you are going to die.” But when a politician steps up to the lectern, the message tends to veer away from death and toward politics.

This was no exception for the class of 2020. While isolated at home in their pajamas because of the coronavirus pandemic, graduates were saluted in virtual ceremonies headlined by government figures and entertainers. Former President Barack Obama celebrated the more than 27,000 graduates of historically black colleges and universities in May, and on Sunday he is set to join Lady Gaga, Malala Yousafzai and others in a “Dear Class of 2020” event hosted by YouTube, a lineup that even the most ambitious real-life commencement would find impossible to replicate.

One class of graduates will get its celebration in person: the 1,000 West Point cadets, who will be addressed by President Trump on June 13.

Tia Humphries, a Howard University graduate from Orlando, Fla., watched Mr. Obama’s virtual address with family in her living room, which her parents had decorated with streamers and balloons to mimic what Howard’s gymnasium would have looked like for the ceremony.

It quickly became clear the speech was not just for Ms. Humphries and her friends. The speech, given on May 16, weeks before Mr. Obama addressed the nation on the killing of George Floyd and the protest movement that followed, still used the momentous occasion as a way to reach beyond the graduates and their families.

The former president made headlines by using the opportunity to criticize the country leadership’s response to the coronavirus. He urged the graduates to take responsibility in the midst of the crisis, when political leaders “aren’t even pretending to be in charge.”

Mr. Obama’s words followed in a long tradition of graduation speeches, landing in moments of national crisis, that are partly for the graduates and partly their country at large.

President John F. Kennedy called for a nuclear test ban treaty at American University’s 1963 graduation. President Lyndon B. Johnson created the framework for affirmative action policy at Howard University in 1965, the year after the Civil Rights Act passed. In 2002, President George W. Bush told graduates of the U.S. Military Academy that the country should be prepared for “pre-emptive action” in Iraq.

These speeches form a presidential ritual as familiar as it is peculiar: addressing the nation through its newly minted adults.

Leland Shelton, a 2013 graduate of Morehouse College, recalled his experience with the personal milestone turned political. Mr. Shelton had spent the months before his graduation lobbying class leaders to pick Ray Lewis, a Baltimore Ravens linebacker, as the commencement speaker. Instead, they chose their president, Mr. Obama.

Midway through the speech the improbable happened. “Where’s Leland?” Mr. Obama said. The president went on to praise Mr. Shelton, a foster care child with a mother in prison who was Phi Beta Kappa and Harvard Law-bound. Mr. Shelton stood up to thunderous applause, listening in disbelief and wishing his mother was present.

But to Mr. Shelton, being included in the speech was also complicated. Mr. Obama spent several minutes urging the Morehouse graduates to be good parents to their children.

“I was thinking, ‘You’re talking to an audience of 550 black men going on to some of the best professional schools in the country,’” Mr. Shelton said. The message seemed to “harken to stereotypes about black men not being good fathers, which I don’t think are true.”

Some political commencement speeches evoke far more than mixed emotions. In 2014, Condoleezza Rice had to withdraw from the Rutgers commencement after students staged a sit-in condemning her foreign policy at the university president’s office.

Kathleen Sebelius, former secretary of health and human services in the Obama administration, was interrupted by a heckler at the Georgetown Public Policy Institute in 2012, and a small group protested her appearance at the university’s front gate. Georgetown’s president said it was the decision of students at the institute to invite Ms. Sebelius as a speaker.

Bethune-Cookman University, a historically black university in Daytona Beach, Fla., had its 2017 commencement interrupted when some students turned their backs on the speaker, Education Secretary Betsy DeVos. Student leaders said they were protesting comments Ms. DeVos made three months earlier that referred to historically black institutions as “pioneers” of “school choice”; they were established at the height of racial segregation.

For Fedrick Ingram, an older alumnus of the university who helped coordinate the protests, the disruption was the highlight of the ceremony. “It was electricity,” he said. “It was almost like 1968 with the Freedom Riders.” The university president had threatened to withhold degrees from students who disrupted the ceremony, but dozens booed Ms. DeVos anyway.

Political commencement speeches aren’t always mired in drama, but for many students and families they evoke a simpler question: Why draw politics into a day that’s otherwise festive and uncontroversial?

That was a question on Michael Agnello’s mind, when the University of Massachusetts, Amherst announced Elizabeth Warren as its undergraduate commencement speaker, in 2017. Mr. Agnello was a fan of the Massachusetts senator, but he knew his more conservative family members would be skeptical of the university’s decision. He decided to bring some levity to the day by creating “Elizabeth Warren’s Commencement Speech Drinking Game.”

The rules Mr. Agnello designed were straightforward. For a mention of “the disappearing middle class,” he advised readers to “fight fire with fire and rip that Fireball.” For a discussion of “student debt,” the rule was to “quell such injustice” with “a nip of Smirnoff.”

But he was not expecting the senator to stumble upon his game online and refer to it directly — which she did midway through her speech, with a reference to Fireball that delighted his conservative relatives.

“By the time we walked out of the football stadium I had 30 texts on my phone like, ‘Oh my God, I can’t believe that just happened,’” Mr. Agnello said. “My family was cracking up.”

Politicians, for their part, realize the difficulties of imparting wisdom to an audience with lots of competing concerns, from family drama to last hurrah hangovers. “It’s always a crapshoot with graduating seniors because a lot of them might have been out super late the night before,” said Cody Keenan, a speechwriter for Mr. Obama.

Mr. Obama gave more than two dozen commencement speeches while in office — at military schools like West Point, state institutions like Ohio State and private ones like Barnard. Over years of commencement speechwriting, Mr. Keenan developed rules of the road. The speaker should be funny and self-deprecating. He should not over-index on the political, even in an election season.

Most important, Mr. Keenan said, is that speechwriters not fixate on producing a speech that becomes an instant classic.

“One of the mistakes people make is that they’re like, ‘I want to break through,’” he said. “‘I want to be Steve Jobs in 2005.’ Steve Jobs broke through because he was dying and explicitly talked about that.”

Kendra Grissom, who graduated from Spelman College last month, was looking forward to the many rites of commencement weekend: marching through the alumni arch, dressing up for senior soiree, passing down the class cymbal. Instead, she said, she spent it propped up in bed watching a parade of digital speeches from “Debbie Allen, some executive from Chase and a basketball player.”

But Mr. Obama offered some assurance for graduates like Ms. Grissom: “The disappointments of missing a live graduation, those will pass pretty quick,” he said. The greatest solace, according to the former president: “Not having to sit there and listen to a commencement speaker isn’t all that bad. Mine usually go on way too long.”