No, it really doesn't. It's a kludge to allow hostile humour against people you don't like, while protecting those you do, all while claiming impartiality.
I feel that privilege is a concept that should be applied to classes, not individuals. You can't just judge someone as privileged based on one aspect of their life.
The whole "punching up" concept just leads to it being accepted to make misogynistic jokes at white women, ablist and body-shaming jokes at "creepy" men, racist jokes at wealthy Asians, and so on.
Rather, I think the intent behind the joke, and the consequences of the stereotypes it reinforces, is what should be examined rather than the demographic on the receiving end.
The problem is that people use humor as a weapon. If you fall those people point a finger at you and laugh while calling you an idiot.
Others use it as a way to deal with stuff or in general just see it as something to make light of a situation. Those people would also laugh but they would come to your help, ask if everything is alright and would help you up. While knowing that everybody falls down sometimes and that it can funny.
Everything can be funny with the right people and that helps to cope.
Dark humor is good as long as it's actually dark humor. As much as I hated the power mods of Reddit, Awkwardtheturtle's constant trolling of the dark humor sub was fucking hilarious. He'd throw random rules on posting and commenting that would take off most comments and posts by default. Seeing those immature assholes lose their shit over not being able to be as racist is hilarious.
Redditor "You like dark humor?"
Me "Yeah sure I guess"
Redditor "I LIKE RAPING BABIES AND MURDERING MINORITIES! I ALSO BEAT MY WIFE! PLEASE LAUGH!"
The problem with racist humor is that theres a limited number of premises. How many ways can you make a slavery or no father joke about black people? How many math jokes can you make about asians? Muslim terrorists? You get the idea.
I dont want the same lazy bullshit over and over. I want my dark humor to be fresh! I want my Titan submarine jokes before the bubbles reach the surface.
Racist humor isnt "dark" humor, its lazy tired rehashed crap. Real dark humor is like kids with leukaemia, it never seems to get old.