This is why I rank DS9 the best of all the spin-offs because that one wasn't afraid to get into the kind of comedic romps that TOS would have. I think TNG could have used more of that, though I understand Berman was very afraid of trying to do that because of earlier attempts like "The Naked Now" falling flat on its face. I don't put down TNG too much for not having as much humor as I'd like, because it does really shine with its own great episodes and I do admire some of the more dry humor they attempted in the last two seasons such as Data giving Worf his cat to take care of in "Phantasms".
You're forgetting that TNG had quite a few of these over the years, they were just a lot better organized and mixed with serious content more fluidly. Take, for example, all of the Q episodes, all of the Luwaxana episodes, Vash, Picard talking down to the Sheliak, and the high tech shenanigans of
Carmen Sandiego.
TNG didn't take itself TOO seriously, but it's true that (with the exception of "The Naked Now") it never really got into the realm of "campy."