@fabiaville It's just something so many people say that many people believe it, it's basically an old wives tale if you want to compare it to some other things in that category. A repeated trope in stories and such as well, obviously. The thing is, there's not really any means to test for its effectiveness while dreaming. As far as I'm aware, the second you even think you might be dreaming, you pretty much start lucid dreaming right there. Awareness gives you some control over the dreaming state. Whether you "feel" anything or not would potentially already be up to you to decide.
Outside of dreams, the reason to do it is more along the lines of verifying you're already awake, as the belief is that you shouldn't feel pain if you're dreaming. So, if you see something unbelievable, pinch yourself and feel it distinctly, then you maybe wonder if you're hallucinating or going insane or something. But again, this is probably something that's more of a story trope than something anyone actually ever does. It's an illogical test in reality as well as dreams, because in reality there are things that can make you incapable of feeling pain. If you're suspecting something might be wrong with you because of something you're experiencing, ignoring the possibility that there's something wrong with your senses in general is dumb as hell.