I'd like to say something, which you most likely already know but it's not very likely that Nintendo will change their mind about Mario Brothers and Peach.
The reason simply is, and I don't mean to be racist, that they are Japanese.
It's pretty common in Japan to be sexist, it's actually very normal. They just don't see it as a bad thing, rather as how it is. You just don't really notice that on the outside because the borders of what's male and what's female are different and the rest will just be seen as the regular sexist things you can find everywhere.
Yeah, she does get those. It's good, I think that maybe with time she can entirely grow out of her reputation as a damsel. But in some games I despise her weapons. I mean, PMS? And in one I've seen but have not played (not a Mario fan so I never play them now) I've seen her using a frying pan (when a princess has access to swords and toys and chooses a frying pan something is off, it was much more undesrtandable and cute in Tangled) and her butt. But yeah, more active roles to both these girls. Happy Peach gets them and hope she gets them more.
Anita never said that they are stupid, silly or weak. She only complains how the plot treats them. I do that often with even my favourite characters. You know, great personality and skills and then the plot gives them only a chance to be rescued or get their behinds kicked. ^^"
And you summed up the entire problem with the trope Damsel In Distress. A female is used as an object to further the male's story. How often do you see men reduced to this role? Almost never and most distressed dudes still have active role in their own rescue. Unless it's used for comical effect. Yes, males get captured or in trouble but you almost never see them tossed away for the entire game/movie/book/story and they prove their worth as active characters in some way. So no matter how great a character, it does not give them much dignity to get whisked away and put in the place of an object; the damsel is the prize in the end. She could be replaced with a cake without the story changing. So that is why I'd like them to have more active roles, especially if the game has little to no other female characters aside from the damsel. How many games pass the Betchdel test? Almost none. I think that giving some spotlight, even as a side kick to the hero or the healer, would make them more interesting. Like, show them off a bit. Zelda already has this cool sacred-power-thing going on, can't wait to see her do more in the future!
But now I have much less issue with the frying pan! I mean, if it is an inside joke and reference it's okay. I always found it funny that a princess did not use a sword. Now I get the point.