He chided them for demonizing enemies and silencing opponents. He cautioned them against a sense of grievance too exaggerated and an outrage bereft of perspective. “If you had to choose a time to be, in the words of Lorraine Hansberry, ‘young, gifted and black’ in America, you would choose right now,” he said. “To deny how far we’ve come would do a disservice to the cause of justice.”

He was by no means telling them to be satisfied, and he wasn’t talking only or even chiefly to them. He was talking to all of us — to America — and saying: enough. Enough with a kind of identity politics that can shove aside common purpose. Enough with a partisanship so caustic that it bleeds into hatred.

Enough with such deafening sound and blinding fury in our public debate. They make for entertainment, not enlightenment, and stand in the way of progress.

His remarks at Howard were an extension of those in his final State of the Union address in January and of those to the Illinois General Assembly in February, nine years to the day after he announced his history-making bid for the presidency. The Illinois speech, wise and gorgeous, received less attention than it deserved.

“We’ve got to build a better politics — one that’s less of a spectacle and more of a battle of ideas,” he said then. Otherwise, he warned, “Extreme voices fill the void.” This current presidential campaign has borne him out.

Obama detractors and skeptics probably hear in all of this a professorial haughtiness that has plagued him and alienated them before. And there’s legitimate disagreement about the degree to which he has been an agent as well as a casualty of the poisoned environment he rues. His administration’s actions haven’t always been as high-minded as his words.

But we should all listen to him nonetheless, for several reasons.

One is that he’s not just taking jabs at opponents. He’s issuing challenges to groups — African-Americans, college students — from whom he has drawn strong support and with whom he has real credibility.

“We must expand our moral imaginations,” he told black students at Howard, imploring them to recognize “the middle-aged white guy who you may think has all the advantages, but over the last several decades has seen his world upended by economic and cultural and technological change, and feels powerless to stop it. You got to get in his head, too.”

Just two weeks earlier, at a town-hall-style meeting in London, hevolunteered a critique of the Black Lives Matter movement, saying that once “elected officials or people who are in a position to start bringing about change are ready to sit down with you, then you can’t just keep on yelling at them.”

Another reason to listen to Obama is the accuracy and eloquence with which he’s diagnosing current ills. In Illinois he noted that while ugly partisanship has always existed, it’s fed in our digital era by voters’ ability to curate information from only those news sources and social-media feeds that echo and amplify their prejudices.

“We can choose our own facts,” he lamented. “We don’t have a common basis for what’s true and what’s not.” Advocacy groups often make matters worse, he added, by “keeping their members agitated as much as possible, assured of the righteousness of their cause.”

At Howard, Obama insisted that change “requires listening to those with whom you disagree, and being prepared to compromise.”

“If you think that the only way forward is to be as uncompromising as possible, you will feel good about yourself, you will enjoy a certain moral purity, but you’re not going to get what you want,” he continued. “So don’t try to shut folks out. Don’t try to shut them down, no matter how much you might disagree with them.”

At this late point, his message isn’t a self-serving one about the political climate that he personally wants to operate in and benefit from. It’s about the climate that would serve everyone best. If it draws attention to the improvements that he pledged but couldn’t accomplish, he’s O.K. with that. It still needs saying.

And so he’s fashioning this blunt, soulful goodbye, a reflection on our troubled democracy that, I fear, will be lost in the din of the Trump-Clinton death match. It brings him full circle, from the audacity to the tenacity of hope.