Though his final episode made the mysterious reason for his departure a running joke, his specials and memoir suggest he was always comfortable with uncertainty.A talk-show host’s final episode is typically a celebration of their tenure, but in his last time at “The Daily Show” desk, Trevor Noah put the spotlight on others, giving sizable segments to each of his correspondents, doing a gushing interview with the comic Neal Brennan and expressing gratitude to everyone from the executives who hired him to the Black women who raised him to those who hate-watched.In a persistently sunny hour, Noah even had a kind word for Donald J. Trump, quieting his crowd by praising what the former president did for prison reform.Noah has always invited others to see him as an outsider because of his background as a South African comic, but his equanimity and preternatural calm also distinguished him. He’s got to be the only political comic alive who could emerge from seven years of regularly joking about the Trump administration and a global pandemic exuding optimism.“The Daily Show” is famous for its topical jokes, but Noah told very few on his final episode. He took a broader perspective. Outlining lessons learned, which included that people were friendlier than they appear on social media, he struck post-partisan notes and said, “Politics turns people’s brains to mush.”He told a story about Jon Stewart calling to offer him the job and saying, “I see you in me.” Noah seemed shocked, and honestly, why wouldn’t he be?Trevor Noah’s 7 Years on “The Daily Show”The host, who took the reins of the show from Jon Stewart in 2015, exposed America’s many blind spots through witty and passionate commentary.Time to Depart: Trevor Noah announced that he would be stepping down in September, citing a desire for a better work-life balance.Saying Goodbye: In his final episode of “The Daily Show,” Mr. Noah told viewers not to be sad and called the night “a celebration.”An Outsider: The talk-show host, who grew up in South Africa and represented a part of the world often neglected by American news, helped his audience see through his eyes.His Best Moments: Noah’s comic perspective set him apart from other late-night hosts. Here are the highlights.Whereas Stewart’s humor ran hot and righteous, Noah always maintained a cool composure. Stewart was at his best in antagonistic interviews, interrogating ideas and calling out nonsense. Noah always seemed eager to get above the fray and treated guests with deference and awe.One running joke on his last show was the mystery of why he was leaving. Discovering that he doesn’t have another job lined up, the correspondent Dulcé Sloan quipped about Noah, who has a Black mother and white father, “Wow, you really are half-white.”You get a hint about why Noah might have gotten restless from his comment that it might be better to wait before developing a take on something you see in the news. But you can learn more about the reason he left from his stand-up. Noah never stopped performing, putting out three Netflix specials during his “Daily Show” tenure, including one last month called “I Wish You Would.”He’s not an entirely different performer in his stand-up — his twinkly-eyed charm is a constant — but the distinctions are revealing. While his specials dig into politics, it’s not the main subject. That would be the slipperiness and meaning of language. Noah is clearly not just obsessed, but tickled by the way people talk and the eccentricity of languages (he speaks eight). His gift for impressions is the centerpiece of many bits.In fact, a premise often seems like just an excuse for him to show off verbal gymnastics, whether it’s pointing out the similarity between the ways Nelson Mandela and Barack Obama speak or showing that to be president you need a strange voice (cue a lineup of impressions). Even my favorite Noah joke, about how trap music sounds like a toddler complaining (from his special “Son of Patricia”), is a virtuosic display that turns ordinary human sounds into a kind of music.Noah’s stand-up aesthetic is also more subtle and wry than his talk-show punch lines. In a joke from his recent special comparing Will Smith’s character in “Independence Day” to his slap at the Oscars, he displays such a light touch that the actor might not have even noticed the jab. (In fact, Smith gave one of his first interviews after the awards to Noah, a booking coup.) There’s a wit to his voice that recalls an earlier era. I would not be shocked to see him become a regular humor writer for The New Yorker.Noah hit his stride on “The Daily Show” when he started speaking more off the cuff. The segments, released online, in which he did crowd work during commercial breaks were often long monologues culminating in metaphors. They showcased his gift for thinking aloud and in real time. What they don’t have is a ruthless appetite for getting belly laughs or winning an argument. The dearth of that hunger is also part of his legacy at “The Daily Show.”On “I Wish You Would,” you get a sense of his temperament when he talks about why people were so angry during the pandemic. His theory is not that Americans were hopelessly divided, but that we were scared. “As humans, we get so comfortable knowing,” he said, emphasizing that last word in his volume and timing, “that we forget how uncertain life is.”This is not just a more existential thought than is usually expressed on a talk show. It’s existentially fatal to a certain kind of talk show. Because as true as it may be, and it is, the job of daily commentator on political events is a lot easier if he at least keeps up the illusion of having a sure-minded, commanding take. Hamlet could never host “The Daily Show.”Noah is startlingly good at appearing confident and assured, which made him a natural at the job. But talent can be its own obstacle. What you’re gifted at is not necessarily what you should be doing. Watching his stand-up, and especially reading his excellent memoir, “Born a Crime,” you sense that he is most comfortable in the moments of not knowing.Talk shows are far more collaborative than they appear. And “The Daily Show” is a machine that can work with different hosts. We first learned that not with Noah but with John Oliver, who had considerable success filling in when Stewart took a summer hiatus in 2013. The years that followed were a catastrophic period for Comedy Central, when it lost a tremendous amount of funny correspondents, including Oliver, Stephen Colbert and Samantha Bee. Noah deserves credit for rebuilding an impressive roster with a more diverse cast.“The Daily Show” will now use temporary hosts, including Sarah Silverman, Al Franken and the former correspondent Hasan Minhaj. As for the permanent replacement, the understandable temptation is to aim for the shiny new toy, but clearly, overlooking your stable of talent has its own risks.Dulcé Sloan has enough spiky charm for a bigger platform. Jordan Klepper displays a bulletproof deadpan. And in their stand-up as well as on the show, Roy Wood Jr. and Ronny Chieng are cagey, argumentative and prolific joke writers who share a delight in the comic kill that would represent its own departure. To my eyes, they should be the favorites. But would either want this grind?In his goodbye to Noah, Chieng set up a joke by appearing to get emotional: “In all seriousness, on behalf of everyone watching right now and from the bottom of my heart, can I be the new host?” More