This common "criticism" of Grice's Maxims isn't one, but a misunderstanding of the Maxims themselves. In everyday conversation the Maxims do hold, that's the p

This common "criticism" of Grice's Maxims isn't one, but a misunderstanding of the Maxims themselves. In everyday conversation the Maxims do hold, that's the point. When they break down, you get "marked" effects — marked is a linguist's way of saying "unusual." This doesn't make the utterances wrong. Violating Grice's Maxims may cause miscommunication, or induce effects such as sarcasm, irony or humour, but also a slew of other, more mundane pragmatic effects. Think of Grice's Maxims not as legislation you have to abide by. Think of them as laws of conversation (law in the scientific sense) which generally hold. I can subvert the law of gravity by jumping. But I need to invest energy, and I will cause an effect which will perturb the current reference frame in all manner of ways. Similarly, I can lie, be facetious, tongue-in-cheek, etc. But that's not the default state of communication. The Maxims aren't there to be obeyed. They're there to describe communication, and also describe non-cooperative communication when they're violated.