It sticks around, but doesn't always work.
It would be a mistake to apply a postmodernist reading to "The Funnies," but for those with that habit of mind it would certainly be tempting. Postmodernist thought rejects, among other things, a hierarchy that would distinguish between "bad" and "good" art. In that sense, a show of cartoon, or cartoon-inspired, art would be of equivalent artistic value to, say, a show of Impressionist landscapes. The idea of "quality" in art was a considered a Modernist fiction that was put to rest by Duchamp in the 1920s and Andy Warhol 40 years later. Lots of cartoon-like art, graffiti art, and political art was taken up by the critical and collecting world in the 1980s and early '90s based on postmodernist ideas.
Yet distinctions persist. There is clearly a difference between good art and bad art, although the which is which can sometimes be difficult to discern. Postmodernism has not survived the marketplace of ideas, nor, for that matter, the art marketplace either. The ultimate postmodernist artist and consummate ironist, Jeff Koons, is considered by the marketplace to be the pre-eminent artist of his generation, the best investment there is.
So take "The Funnies" at face value, as a collection of pieces by artists who share an affection for cartoon and comic art, and enjoy it, or not, for what it is.