No doubt part of Colbert's cancellation was due to political pressure from the ownership of the network to please Trump so this new merger they want will go through, but I also think, as others have pointed out, that Colbert's cancellation was also due to the rapidly changing television and entertainment landscape. The Late Show has become a dinosaur in that it has a huge and expensive staff but draws relatively low ratings, and in an age where cable and satellite TV is dying and with network cost-cutting shows like Colbert's simply aren't going to survive without major changes to how they're structured. And that also likely applies to Kimmel and even The Tonight Show, although I suspect that NBC would be more unlikely to cancel it given its long history and somewhat higher ratings. But there will likely be substantial staff-cutting even at those shows.
Gutfeld's model works because, as the article posted by heelinhell points out, he has a much smaller staff and much less expensive setup, and because he gets a huge advantage from following Fox's highly-rated primetime lineup of Watters, Hannity, etc. The guy has a large built-in audience that these other late-night talk shows no longer have as local TV news becomes less popular and the traditional TV networks continue to slowly fade from the landscape.
And I also find it amusing reading conservatives who claim that Gutfeld is popular because he's funny. No doubt Fox viewers who love watching Hannity and Watters find him a riot, but I doubt very many people outside that audience do. I mean, this is a guy who less than two weeks ago actually said on Fox's "The Five" what I listed below - and that counts as a pretty good sample of what qualifies as "humor" on his own show. Yeah, he's just a real barrel of laughs, that guy.
"During a debate on the Fox News show, Gutfeld addressed how Maga-supporting conservatives often get branded “Nazis” and he then compared the term to the N-word. “The criticism doesn’t matter to us when you call us Nazis. Nazi this and Nazi that,” Gutfeld said on air. “I’m beginning to think they don’t like us. I’ve said this before. We need to learn from the Blacks. The way they were able to remove the power from the n-word by using it...You know what? I’ve said this before, we need to learn from the blacks. The way they were able to remove the power from the n-word word by using it. So from now on it’s: What up, my Nazi? Hey, what up, my Nazi?"