I think focusing on Noah is ignoring that the entire staff is completely different. All the correspondents used to also be the writers and look at where their careers have gone. Stewart didn't write things, he was an editor and performer. From what I understand Noah writes far more of his stuff. I don't know if Noah has the same level of control Stewart had over who the writers were but I assume it's still pretty darn high.
Stewart picked Noah in part because he thought the show and the media and everything was going to take on a more international focus and the show needed that kind of voice at its head. He never anticipated a President Trump nor what our media has done in response to that becoming even more insular. Even a fake foreigner like John Oliver tries to avoid straying too far into such issues outside of stuff like Brexit.
The Daily Show, as it was, was also a product of its time, now there are so many internet channels directly inspired by it even if they're limited due to being one man operations. I mean, that's the joke in the name of Last Week Tonight originally, that there's no point in covering this kind of shit in a form of immediacy because you likely just marinated in it all week or all month or whatever.
