For the most part, what you seem to be thinking of is observational comedy: pointing out the absurdities in life that people just sort of take for granted and never really talk about. This is not mutually exclusive with satire of empowered individuals, and in fact there's a lot of overlap. George Carlin was a brilliant observational comedian and he frequently pointed out the absurdities of empowered groups.But the most revered comedians talk about everyday life situations more than anything else. Relatability is key.
My problem was with your initial claim that nobody punches up because nobody can relate to it.