There are endless scholarly debates as to whether the comedy news programs are good sources of news or not (and whether their viewers are better informed than other segments of the population, or not).
I suspect that the public could care less about these debates, and just enjoys these shows because they are funny, if often also a source of valuable information.
Much of the evidence and analysis that I've seen (see for example Jeff Jones' Entertaining Politics and this Annenberg Public Policy Center Report on the Colbert Report) indicate that these programs provide outstanding news coverage, and that people do learn from watching them, especially if they watch them to be informed, as well as entertained.
We can think of these programs as the proverbial broccoli with cheese sauce. They taste good (at least unless you hate broccoli like I do) and they are good for you as well.
But these programs have a critical flaw, at least if someone utilizes them as a primary news source. They simply don't cover many stories.
The Daily Show produces roughly 23 minutes of content per night, four nights per week. Of that content, usually six or seven minutes is devoted to an interview. That leaves a maximum of 1 hour and 8 minutes per week for covering the news. What Daily Show covers is covered well. But, typically, Jon Stewart only covers one to two stories per night.
John Oliver's new Last Week Tonight is an even more egregious example of this paradox. Oliver may offer the best long form public policy television journalism being produced today. His lengthy deep dive pieces on meaty policy issues (see these pieces on net neutrality and payday lending) are fantastic, educational, hilarious, and unmatched anywhere else on television. Yet, Oliver only produces one thirty minute show per week, which leaves, at most, time for two to three of his lengthy segments.
Additionally, these late night comedians often go on vacation for 1-2 weeks at a time, leaving reruns or other programming to air in their time slots. During those periods, someone who relied on these shows for their information is left without coverage (which never happens on traditional newscasts).
Thus, I've come to two conclusions regarding these programs. First, they often produce better, harder hitting, more honest coverage than traditional television journalistic outlets (especially the slanted screamfests on cable news).
Stewart, Colbert, and Oliver are happy to point out bullshit, and are less constrained by the journalistic need to appear nonpartisan and unbiased (which often leads to false equivalencies, or to the reporting of worthless partisan talking points in an effort to be evenhanded) than traditional journalists (this is not to say that there aren't some fantastic reporters out there, because there are many of them).
Indeed, I think that the comedy news programs provide a great model for how television news ought to reinvent itself in the era of 24/7 news cycles where everyone has either already read about a story on twitter, or gotten a cell phone alert about it before they sit down in front of the television. Add an original reporting component to the comedy news no BS model, and you have a product that would be attractive to many cynical, frustrated younger Americans.
In fact, I've frequently mused that my choices for moderators for the next set of presidential debates are Jon Stewart, Jon Oliver, and Howard Stern, who is a similar sort of interviewer (yes I recognize that no candidate would sign off on this group, and that it lacks diversity).
But, crucially, young people cannot be satisfied to get their news primarily from these sources because there are simply too many critical stories that they don't cover. The hosts also don't feel the same obligation that the best mainstream media reporters do to keep their viewers well informed.
Rather, more like talk radio hosts, their eye is on entertaining, even if they also care passionately about public policy and work hard to get stories right. Their priorities mean that viewers might not hear about the most important story of the day, but rather the one that lends itself best to comedy.
It's best to consider these comedy news programs like dessert— perhaps the best part of a meal, and certain worth having, but no substitute for an entree (at least not unless there is the comedy news equivalent of an entire pint of Ben & Jerry's).