The issue with standard characters is that they are uninspiring. Solid Snake, the protagonist from the Metal Gear series, is literally breed to kill. From the onset, it's revealed, he was part of an experiment to make the 'best' solider, spy, and ladies man. He's also very intelligent, quick thinking, skilled, attractive, and overwhelmingly cool. Metal Gear Solid hasn't shown its age very well. The first generation of cutting edge 3D graphics from the Playstation era don't have the same punch they did 20 years ago, but the writing is beyond even most games today. The gameplay, while broken, does stand up better than expected. The game is just butt ugly.
Solid Snake moves effortlessly from killing terrorists to sweet talking pretty ladies and then laying down some crazy philosophical soliloquy. He's awesome, but lacks flaws. Anything that Snake does wrong is a mistake he couldn't have avoided. Often his biggest challenges are something he's prepared for. It seems like every character surrounding Snake is heavily flawed and fixed by his presence. He's a mystical, walking solution to every problem. Playing as Snake is an amazing experience, but incomplete. He's so far from human (purposefully, most likely) that he's totally unrelatable. Ultimately, I can't help but say that Snake is a failure as a character, but the escapism of being him is intoxicating.
Three adventures later, in Metal Gear Solid 4 we find snake weeks away from his deathbed. At the relatively young age of 42, snake resembles a man 20 years older than him. His rapid aging is the result of errors from the experiment that created him. He's dying and can no longer function like he did even a few years prior. Often he looses control to coughing fits, looses his ability to walk temporarily and suffers from what seems to be a heart attack. He's weak and dying, but that doesn't stop him.
Here, Snake is an unstoppable machine, even more learned and deadly than he was during the events of Metal Gear Solid. Snake is flawed, not just by his physical ailments, but also his lack of trust. Snake from earlier seems naïve in comparison. Snake now, more than ever, is hardened by the lies of the government, the traitorous nature of those who used to be his friend. He also must overcome the difficulties of learning to trust shadier crowds to further his own cause. Snake is less willing than ever to save anyone because he doubts how just his actions are and if they'll mean anything. He struggles with his growing irrelevancy of himself and his perspective.
Snake is even more amazing than ever because he achieves what he thinks is success despite his flaws, and maybe even because of them. Snake saves the day in his own way, but not because he wants to leave a mark or be important again, but because he wants the world to be a better place for the next generation and live out the rest of his short life in peace. His actions and words are more compelling and bigger than the discussions and philosophical arguments made at the beginning of the series. The result is much more powerful because now anyone can see a part of themselves in Snake and he's still amazing, well trained, and super smart.
The Metal Gear Solid series has much more to offer than this, but just taking a look at Snake makes a point against most games: the characters are boringly perfect or terribly written heroes. Snake himself is the image of the perfect man; even in Snake's old age, he's massively ripped. Escaping the idea of having a fit hero is one that's not easy. If Snake was a chubby, out of breath teenager he'd be totally unbelievable. So fixing the image isn't so easy as fixing the character themselves. With men, however, this issue isn't as important or pronounced.
Booker DeWitt is the hero of Bioshock Infinite, a game that I haven't played. The main draw, or at least the thing I hear about the most, of Infinite is Booker's companion Elizabeth. Apparently her relationship with the character grows and is important to both the gameplay and the plot. I don't know much about the game itself, but I can say that while Booker is a kind of weird looking guy who learns alongside the player about the mysterious world of Columbia, he's still just a badass who takes names and saves pretty ladies. Elizabeth's role as a secondary character is one repeated throughout all games.
Strong female character are rare. There aren't any Girl-Solid Snakes out there. Often the only flaw a female character has is their lack of a penis to pull them around everywhere or a total lack of sympathy, tact, or intelligence. This isn't to say that there are not strong female characters or well written games. Most characters fail the litmus test of real flaws or reliability. Someday, maybe someday soon everyone can be like Solid Snake.