Hm.
I think all is not that bad. Why? Because, I think that in all this "objectification" of women or stereotipization of men there is one important parameter missing: POWER.
You see, I have a friend, who's a girl, and a gamer. And yes, she likes Lara Croft very much, thank you. Yes, she sometimes finds useless babes in bikinis distasteful (on TV) - and sometimes she finds them empowering, but I've never heard her complain about the same thing in games. She takes pride in her slender, bettered version of herself in Dragon Age: Origins. (Who doesn't?) My point is: what do you all think, WHY do so MANY girls (and women) sometimes enjoy the "sexy" roles assigned to them by, well, the world in general? Or why do we, men, enjoy our roles of heroic soldiers, commanders, and one-man-armies?
Because it promises POWER. See, they're objectified, but ultimately - who isn't? Aren't males objectified too? One of the things because I never got playing Gears was the stupid, unrealistic, hilarious typification of every single male in that game as a Manbearpiggish thing on steroids - but how MANY guys actually enjoy Gears? MANY, I'd say. Why? Because it fills their need for power. To me, that amount of power was just comically hilarious. Maybe I have a tad bit more self-esteem, maybe I lack it?, I don't know, but that form of "Powerful Me" didn't appeal to me. It felt like a joke, and making fun of guys in general (now I sound exactly like a feminist, but I'm a man, see? So it goes both ways.)
Coming back to girls (referring to both stereotypes and real life): what's the one, ultimate way a girl can win over the heart, the mind, and the body of a potentially brutish, insensitive, selfish guy (or even a normal, sensitive, generous guy)? The only way is to get HIM to want HER. Often times, disregarding the cost. So, the ultimate Power for women stems from their absolute appeal with which they can seduce men, from women's ability to be WANTED; men being, arguably, the most powerful beasts alive (at least physically). But only after women, I'd guess, because they can (mis)use us pretty badly.
And while we do it out of generosity, or the naive need for romantic love, and some silly chivalric ideals (I've been the victim of all those, and still am), some women are doing it, sometimes, from the sole need to dominate over men and feel better about themselves.
I'm gonna go a bit off-topic:
Been burned that way. A girl told me, I quote, "But you're, you're too special, too smart, I just don't enjoy a relationship in which I can't... dominate. I don't feel special when I'm with you, I feel completely ordinary. I want to be with someone I can dominate and feel superior to." Despite the fact that, to me, she was the most perfect female human being alive. I'd bow to her feet, if she would let me. But then again, that too would seem superior to her.
Now before someone rushes to say, "Ha, you must have insulted her or been a stuck-up asshole" or whatever of the sort, I'd like to remind that I was the one liking the girl, in love with the girl, and trying to get to her, etc. And, no, I didn't bother her. We weren't speaeking for months, it was fine with me, and she called me. It appears that her ego needed some food, because eventually she resorted to lying to me, pretending, manipulating me, just so she could feel victorious "over me" (in her words, "NO! You're wrong! I'M RIGHT!"). And guess what, she felt no remorse about lying. And, she confessed to lying and sounded rather proud of it. To her, it was just another way to get her things done - whatever that was. And lying was, is, something that makes me cringe.
/ends rant
So you see, sure, women are generally the "weaker" sex, but men are "corruptible" in the sense that they can rarely muster the power of will to reject, or deny, a beautiful, intelligent, sensual woman. For girls, using their "assets" is like the ultimate mind-control weapon.
So, while many girls object to the objectification (I'd say the more precise term is "focalization" of what makes them powerful), many girls also like it and feel comfortable with it - often, this feels much better if their high heels stomp men's hearts, or something of the sort. And that spells: p-o-w-e-r. If women didn't like objectification so much, guess what, they wouldn't be doing it themselves. But look around on Facebook, or in town, and count the number of girls resorting to "self-objectification". I for one, think that at least 80% of girls are using their potential "sexyness" to increase their appeal to whomever's street they cross (or whoever glances their profile pics).
And we men do it too. Maybe not me so much, but how many boys out there are being intentionally loud, rude, or showing off their stregth (pushing other guys, whatever)? Many of those. If a girl gets hurt by such a guy, she calls him a "jerk", and if a boy gets hurt by a foxy lady who doesn't like him but likes his attention anyways (mildly put), he calls her a "*****".
And the quest for Power, can make each of us a jerk, or a *****.
So about all of this objectification thing - if it exists, it's necessary, and it's there for a reason. As some famous person put it, "Stereotypes exist because they have grounds in reality."
So, I believe, it's only human nature. If we could, we'd have the hottest, most gorgeous girl possible. But we can't, so we project - at least ourselves, as the princes. And girls would have their princes, all right. But they can't, so they project themselves - into beauty queens.
You can't be a girl and not want to feel wanted and beautiful, I guess. You can't be a guy and not want to be the knight in the shining armor, or the heroic super-soldier saving the fates of millions and "earning" his bride. Sure, these yearnings are interchangeable, but empirical data would dictate that girls are more likely to associate with the former, and boys with the latter.
It's a fairytale recycled. And we know that everyone's perfectly perfect in fairy tales, don't we?
And there's nothing wrong with wanting to be perfect. After all, it's one of the goals that make life worth living. The problems start when we imagine we're perfect, instead of acknowledging our gray reality and working on it, painting it.
And it comes full circle - part of that "painting" is us, enjoying our colourful alter-egos in the lush, imaginary worlds of video games.
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P.S. What's a White Knight?
P.P.S. I think that maybe we should discuss about porn entering the gaming industry. Because, after all, objectification is oftentimes porn, and hell - aren't babes in bikinis touching themselves and dancing sensually some kind of soft-core porn / erotica? Which everyone enjoys at some time, though. Girls and Boys. Maybe we should panic about girls in video games in the same way that we panic about girls in porn. Which is like, not panicking at all, because it all comes down to a specific artistic expression, which in turn is - normal.
P.P.P.S. I, for one, would like to see more girls gamers! And no, objectification isn't what's repulsing them. In fact, it may just be the thing to attract the broad masses of girls who can't associate with a game unless it has some pink costumes in it.
P.P.P.P.S. I realize I've over-generalizing, maybe, but that's why I have many "some / sometimes / maybes" in my post after all. So please don't go nitpicking.

And I apologize for the use of CAPS instead of bold/italics, I'm just not familiar with the formatting commands here (Can anyone point me where to find the rules? Thanks.)
EDIT: I still can't understand why many guys admit they choose to play as female characters in games. Curiosity, sheer boredom, or...?