The whole "damsel in distress" thing plays to the ages old male power fantasy. Typically our male ancestors were hunters, protectors, and providers. Naturally we've evolved to play out such things in our heads as a means of survival. How many times have we, as men, fantasized about saving the day during some anecdotal catastrophe where we were then looked upon as the object of some young women's eye? Of course pop culture throughout time will play on that, and as long as there is red blood in our veins it will never go away. However, it is incumbent to our continued evolution that we recognize such tropes, and try to be more sensitive.
Btw Sensitivity & censorship are two entirely different things in my book. If you wanna make a game, book, or movie about saving a princess you shouldn't feel insecure about expressing yourself artistically. Just be mindful that there may be men & women that experience your work.