No, I would definitely hope that they don’t start as genderless. Because gender isn’t a cosmetic difference, like hair color or (for the most part) skin color.

I disagree with you.
The way I see it, the biological differences (the obvious physical, sexual differences) are the only inborn ones. The rest is a matter of cultural upbringing.

Yes, we live in a society where I'm looked down on for not wearing makeup, dresses or high heels, or for not shaving my body hair. But that doesn't make any sense, and I'm glad I grew up in a country where the concept of "cooties" doesn't even exist, so that when people ask me "why don't you do all these stuff society says women should do", I can answer "why would I?" instead of "Oh I'm sorry, I forgot to play the role that's expected of me, getting back to it right now".

When I grew up, I played wrestling with my brothers, we played with our toy guns, and we played with our dolls and plushes, and we played videogames. All four of us grew up as completely different individuals, with different characteristics that could be considered "feminine" and different characteristics that could be considered "masculine". My eldest brother and I are more quiet, introverted, "read-a-book-in-your-room-all-day" kind of people. My middle and younger brother are more extroverted and active. My younger brother shares my interest in collecting coins while my middle brother shares my love for cats.
My mother is strong-willed and, if I may say so, rather bitter. My dad is much better with people, especially kids, as he is more caring and more patient. My mom enjoys playing videogames, knitting and weaving. My dad likes opera, rugby and cross-stitching. My mom cooks wonderfully while my dad is pretty bad at it. I inherited that from him (that and his stupid sense of humour. Thanks dad). Fortunately my husband is a great cook, just like his own mom, who taught him.

Can you see where I'm getting at? We're all people. We have characteristics and interests that are ours. I don't really care which are considered feminine or masculine, for me they're all neutral anyways. Why would it be weird that my dad enjoys cross-stitching, but normal that he sews up people? As he says, it's basically the same thing (oh, right, my parents are both doctors by the way. Is that a feminine or a masculine thing? I've lost track at this point.)

If you live in a society where different things are expected from males and females, then humans will develop to fit what's expected of them, or feel out of place. Or, really, both, because the way they're made to act doesn't always happen to perfectly match the way they feel. If it does for you, good for you. But I'm sure any study you pick would show you that most people feel inappropriate for ridiculous things. I had a friend who thought she was malformed for years simply because breasts are always shown as erect, and hers weren't always that way.

So, do I feel there is a difference, nowadays, in how males and females are portrayed in the American media? Yes. But I think that's a problem. As Lena said, most men are not tough, emotionless superhumans. It's not more unrealistic if you make that tough, emotionless superhuman a female, because they have nothing to do with an actual human being anyways.
And these games aren't about being realistic. They're about playing as someone who's much more awesome than you are. If I want to play as someone who can make huge leaps and punch through walls, does it have to be a male?

We're talking about females here, but the irony is that my main concern is the other way around. That is, I want healer/support-type characters to be playable as males. Males who are sensitive, compassionate and not about brute strength. Because that's the kind of guy I'm attracted to, and I want to be able to spend time with one. But by pushing the genders in codified categories like that, you're saying I need to play as a female or as a tank guy, neither of which I have any interest in.
At least I can play the female support and identify with her, so I wouldn't be happy if the support had to be male, either. I like being able to play both. Incidentally, if I play the tank, it will probably be as a female, so I can at least win on one of the two fronts (identifying and being attracted to) rather than lose on both.

Anyways, I feel like we have drifted from your original point here. Which I think is "since male-oriented games should have male characters as default, to have more female characters, we need more female-oriented games".
What would you consider "female-oriented", though? A game that's not about speed or fighting? A game that relies on things other than physical strength?
Would adventure games fit that bill?
But then, to be "balanced", does that means adventure games should have female leads by default or have a good reason not to? Or does the "male = default" apply to all videogames?