Do men like women who need to be saved?

I was chatting with my friend discussing what men can see in some women. Some girls are ridden with fluctuating emotions, crazy past experiences and an insane 'he's-got-a-restraining-order' boyfriends. My friend and I are two relatively grounded, secure, content, problem-free females (with no insane ex-boyfriends might I add). We can chat, have a laugh and be good friends with males. But does it just stop there? Does our first impression just slowly fade away? Are we lacking the contagiousness of damsel-in-distress-itis?

Damsel-in-distress-itis: Commonly known as Cinderlla-syndrome. When a female, suffering self-inflicted or other trauma, exudes an alluring waft, attracting heterosexual men who seem to have no other choice than to save them and conquer trauma. Damsels in distress (DID) can be found crying in stairwells, putting broken hearts in their display name or wandering the gutters with a broken high heel.

Do women have to be going through a bad break up, suffering from a broken friendship, depressed in some way, to attract men? I accept the fact people bond over deep and meaningful conversations, over late-night phone calls, over crying on shoulders, but does mean the plain, happy damsels (PHD's) miss out? Now back to personal experience, I've been a bad person. When I get mad, upset, stressed, suffer some sort of drama, I just feel the need to "accidentally" tell Mr X, which is what we shall call him. I just have this idea that if I open up, be vunerable, ask for advice, trust him with my emotions, that this will allure him, flatter him or somehow rub off on him. But I never have, because it's insincere on many levels and I'd be doing it for all the wrong reasons. Plus, my depressing moods never last long enough for me to cry to him anyway.
But is the waft of a DID insatiable? And do the PHD's get overpowered by the strong scent that seems to follow these females around?
But maybe it's something more general. Maybe, if a man can get a woman through saving her and making her happy, its like the relationship version of working for and earning your first $1000. Maybe the relationship just feels more special, knowing that the man has helped out a poor, delicate girl. Or maybe the PHD's give off a different waft; a waft that doesn't seem to need help... or a man. PHD's are repellents! Independent, self-assured women need lovin' too. I guess they just don't go crying about it to everyone.
During the conversation with my friend, I also brought up another point: 'I like to save men though'. And, after saying that, I've learnt so does my friend. It's always nice to save a guy. You feel useful, acknowledged, important. I want to be the girl that he opens up to, that he cries to, that he depends on and confides in. Maybe the PHD's have another purpose; to save the men who aren't too busy saving the DID's. DID's are used in questions, to signify uncertainty, the unknown, even allure and magnetism, but PHD's are there to save lives, no matter what. And, to quote countless TV doctors, "They don't call me a PHD for nothing".