In a CoG type of thing I think the damsel would still have to have some kind of strong supporting role. Like maybe as a healer/doctor they can patch up their hero easier increasing their durability. Or as a engineer/techy they could develop/improve weapons for their hero. And of course some choice on how the story progresses. I think it’d end up pretty dull if you played the damsel and just wobbled along as the hero did all sorts of things while you floundered in the background. Especially if it’s the type of damsel who needs saving because they have 0 self preservation or are just always mucking things up and needing help.
Otherwise yeah, I don’t mind playing a damsel. I like it in some smut books when done well.