Laughter v. Happiness?

Watching Burr's performance, "Why Do I Do This?", on Wednesday, one thing still sticks out to me. It was obvious that on one point, he has his jokes locked and ready to go. Then he tested the audience and the audience wasn't responding the way that he wanted them to, and he had to regroup a bit. This probably happens with other stand-ups, no doubt it does to all of them at sometime, but this is the first of it that we have really seen in the videos we have watched. The particular issue that he has to skip over because the audience wasn't responding was unhappy families. In their rejection of his jokes, he replies, "You must all have happy families, huh?". Typically, from what I have seen previously, the audience responds to a joke like this a little bit. His audience was rather cold however and it was more of a time wasting sentence while he regrouped and transitioned or locked and loaded his next set of jokes.
This led me to the question: If everyone were happy, would we laugh less on the aggregate? It seems like a paradoxical idea, but much of the comedy that we have seen has been a response to evils and wrongs in the world, some more light hearted than others. For example, in George Carlin's newer stand-up (the one with the grave stones) his main concern is consumerism. If people were happy with the way things were, no one would be laughing. If there wasn't a problem, namely consumerism, what would Carlin joke about? All of Carlin's stuff is about some sort of problem. His most famous stand-up act is about the problem of language and "The Seven Words You Can't Say". Problems make people unhappy, but comedians offer relief from that unhappiness with laughter. Idiocracy functions on the same "making a problem funny" model.
This particular type of comedy seems in line with Freud's idea that we laugh in order to deflect pain, to not really deal with overwhelming problems, and thus we don't develop anxiety disorders and such. If we don't have these problems however, if we don't have at least small anxieties, if everyone is happy then, how does Freud's theory work? Would there be no laughter in a totally happy world? Laughter and happiness seem to go hand in hand and it is odd to think that one could oppose the other.