First, Neonivek.
Most of the time, in the vast majority of games, the character's gender identity is not important to the story. It just isn't. Most of the time, in a shooter game, or an action-adventure RPG, or hell, Laura Croft games, or Metal Gear...the character could be the opposite gender, and it would really make zero difference to the plot.
Also, your example is incredibly flawed. To swap their gender is the equivalent of teaching children that a woman could also have led the American Revolution (if there was not such rampant sexism at the time), because gender really doesn't matter as to someone's capability and competence at a task.
Now Leafsnail.
My definition of strange is that you think it shouldn't be like this, that the setting is somehow wrong for switching gender roles like that. Otherwise the default is sexism against women in the game, which simply isn't necessary. But that wasn't my point anyway. I'm saying that if you try this for any given game, and then the game feels unplayable or the plot no longer makes sense etc., there's something wrong. Because in most cases, gender identity isn't all that important to the plot, unless pregnancy or sexism are also integral to the plot.
But in any case, seriously, why not? Why would it be bad if there was Larry Croft too? Or Solid Snake was a girl? Why couldn't Maria and Luigey go to save Prince Plum from Bowseria? You can say it makes them into a different character if you want, but it really doesn't. The only thing it changes is the gender. And yes, I know that's a large part of identity, I have personal experience with it, but when it comes to fighting? When it comes to saving people? When it comes to getting fat lewt? Gender doesn't matter, and it shouldn't matter in games. Because when there are so many more games with must-be-male protagonists than games with must-be-female protagonists? There's something wrong with those demographics.