First, allow me to focus on a few points.
After all, the protagonist, the male, is the one who has it worst. He's the one who has to put himself at pain, and even die, over and over again, in an endless cycle of torment, for the benefit of the women.
Well, the obvious answer would be to create more women so males don't have to shoulder the burden so often! ... no, there's no sarcasm, there.
Yeah, 'damsels in distress' tend to be shallow characters without much agency, but who has less agency than the protagonist? The one that can't so much as lift a finger if the player doesn't press a button telling them to?
I've said it time, and time again, NPCs have zero agency. None. Their only agency is to react to what the player character does, frankly. An innkeeper in a game will often never, ever, ever leave their post, no matter what. Unless you wanna argue that it's what they want to do to be statuesque beings that only rent to the player character while they're on screen, then they have zero agency.
Meanwhile, lets, say, Link, is off to save Zelda (who's not all that important to the legend of zelda as she's been absent in several LoZ games), but he's in no way programmed/forced to do that. Smash pots, fish, faff, run into a wall for an hour. While Link may lack a brain, the player that fills his role, and takes Link up as an avatar in that world can go do what ever, and often no 2 Links will go through their quest to save Zelda in the exact same way. Each as special as a snowflake.
NPCs, on the other hand, don't get this option. This isn't Reboot, or Tron, here. NPCs don't live lives off screen that we're unaware of, though some games are decent in giving that illusion.
The plot revolves around the player character. The quest will not get finished without the player character. An NPC might help, but the responsibility of saving whatever will revert right back to the player character once the NPC helps out, usually by flipping a switch, or giving an item, then they're done.
Said player character is often the most capable being on the entire planet because no NPC is usurping the role of finishing the game. That's power, imo.
Player Characters have the true power of the game, and they have the agency to use it as much as they can as the player fills the player character with their will.
While there's only 22% women in the gaming industry, according to a recent Game Informer magazine, there's not really much of anything stopping guys from making female characters, be they PC, or NPC (Except the rest of the gaming industry, really. Can't imagine when the public got to shout at a developer to have gender changed), since Lara Croft, and, well, pretty much every female character in gaming was created, scripted, but thankfully not voiced by a man.
Books, and movies, too, make the excuse of men being unable to write women a bit of a joke as most movies are written by guys, even Rom-Coms. Sure, some might have problems, heck, most might, but it's hardly an excuse.
If it's so problematic creating a female character, then, well, hire an expert. Women, someone who can write for them, etc. One of the most important parts of getting women in the industry is them getting hired, and hired for the right reasons.
I mean a lot of games are in fictitious worlds where weapons, armor, and magic can more than make up for anything. Relying on biological weakness seems kinda like bullshit when fireballs incinerate an enemy with ease, and metal protects people all the same, and a blade can cut regardless of who wields it, or a gun can splatter someone regardless of who fires it, and super human strength, and durability's the norm.
They might have basis in a real world, but game physics/mechanics/etc. trump all of that, IMO.
On to the question that is the title.
No. We should have stories where it's focused on the gender of the character. The problem is, it's a bit to common that it focuses on men.
Like Yahtzee says, there's almost no games out there where being a woman is relevant. Males get treated better than that.
But if there's no point in the gender one way, or the other, then why not have both genders be available? Make your work a bit more welcoming in exchange for it being shallow? Of course its optional, but expecting people to like it when you only pick one gender when the plot doesn't call for gender, is not going to go well.
I mean, I was sitting out in public playing Senran Kagura (I gotta stop doing that), and into the building walks a family... with kids.
One of those kids, a boy, wanders up to me, and leans on me, and looks at my 3ds screen, and says "You're playing as a girl? I like playing as boys."
I was annoyed... not that he had a preference, rather that he invaded my personal space, and it was kinda awkward.
I don't really care what a person prefers to play as, I'm all up for the having the opportunity, just as much as I want the opportunity.
Honestly, it's as simple as that some times. We just want to play our own gender, or the opposite gender. We just want to.
If you wanna fault me for wanting to play my own gender (female) a little more often than we get the chance to, especially in games where gender matters, then sod off!