Jon Stewart took over a nondescript comedy show and turned it into a venue that aired some of the best political satire on television on nearly a daily basis for about a decade and a half. In a world where politicians and the media that are supposed to cover them seem to compete with each other over who is most morally bankrupt, most corrupt, most cynical, and most stupid, Stewart's show provided moments of relief and sanity and common sense, packaged as comedy around a body of top-notch research.
The Daily Show used to be extraordinary. It spawned a few other shows where former cast members explored interesting variations on the theme of satirizing public life, and might have created or defined a genre in the process. Those days are over.
I tried to like its new host, Trevor Noah. There is a phase of comparison anybody in his position has to overcome, where he is seen as replacing somebody rather than simply a voice of his own. There are all these small differences, some deliberate, others maybe not, that might annoy old fans just because they are different from what they are used to, and wouldn't have been even noticed otherwise (the out-of-breath voice of the announcer in the opening credits, introducing the Moment of Zen standing up, ...). It takes a while to find one's voice in this kind of job, and Noah still looks like he can't quite believe his luck, or how funny the jokes are (even when he messes them up), but it took Stewart a little bit of time to find the Zone of Anger at "the system" necessary for his brand of satire, so maybe Noah just needs more time to get there. All of these things are fixable.
A more serious problem, I think, is that Noah is moved by something less interesting than Stewart. When news people, cornered by public opinion that trusted a comedy show more than what they tried to create, "accused" Stewart of being their (biased) competition, he would insist that his primary motivation was comedy based on the absurdity of the system, rather than a specific political agenda. Many (especially conservative) folks dismissed this as a tactical response, but I think it was essentially true. Of course most viewers of Stewart's show would be "liberal", but I think it could have been watched and enjoyed by a conservative, too, for its irreverent criticism of across-the-aisle stupidity and callousness and Stewart's non-partisan sense of fairness that allowed him to have many productive and interesting conversations with people he deeply disagreed with.
Noah's show is different. His primary motivator isn't comedic wonder at the theater of the absurd that is American public discourse, but a specific political view. He wants viewers to think about things in a certain way, and he has little to offer to those that don't. Where Stewart's classical foe was Fox News, Noah just piles on the Trump, an easy target, but without its refraction in incompetent and biased media only of passing comedic value. Of course, Trump would have found a prominent place in Stewart's show, too, but while we enjoyed laughing at his antics, we would also have learned something about how his story was told to us by our media. Noah tries to emulate the taste of Stewart's show, but without the fiber. He has lost the essence of TDS because his interests are essentially different from Stewart's, and we are just a little poorer for it.