So I had to look up the term Mary Sue. Never actually heard it used before, but have seen the characters plenty of times. I haven't seen many true Mary Sue's, young girls doing extraordinary feats that are in actuality impossible for them, but have seen plenty of characters with those flawless personalities. The player expects that every challenge their character faces can be overcome and that's just not the case. I see it currently in my tabletop games I run. My players refuse to run from a fight or give up on an investigation, even if I stonewall them at every turn because that is what I wanted them to do.
Sometimes, it is in character. The character truly believes they are capable of anything and will never back down. That perseverance can even be the driving force that does force them to succeed, with a lot of out of game luck. However, no character should be perfect. There is no suspense to it. In one of my 1x1 games, my main character is currently dying from a poison because I found it far more fitting for him not wake up as the evil witch assassin hovered over his bed. He is also extremely prejudice towards other races, so the dealings with the goblin kings haven't been going too smoothly.
I've recently got involved in local tabletop games and they have greatly increased my understanding of character development. As Darkmatter says, we were all Mary Sues once. You jump into a game where the CS is designed for you to make it as strong as you want and the temptation is just there. Why not be a total badass since the only restriction is your imagination? You can take down that iron golem in the first post because you can write out a clever attack and control how the golem reacts. In a tabletop, that's not the case. You start out in a weaker state (most games) and the dice (luck) are the ultimate factor of how strong you are. Most games also strongly encourage taking character flaws and disadvantages. Obviously the weaken your character in some way, but the game gives a reward for being so bold and a flawed character is far more interesting than a perfect one.
It is one of the reasons why Female Shepard of the Mass Effect Series is one of my favorite video game heroines. She is skilled in combat, but due to the story line and the luck of the draw, she can't overcome every obstacle. For every victory she achieves, there is often a loss to go with it in some form. Not many characters in general can give us that experience, let alone females.
....and now after that thought process, I really want to dig up one of my RPs where this was the whole point of our characters. They couldn't overcome most obstacles. The real challenge was how they dealt with the personal and environmental fallout of those obstacles.