I can do it well enough when my character doesn't talk. I self insert into Fallout and Dragon Age: Origins without a problem, but I never feel like Commander Shepard is me. It usually feels more like I'm assisting in writing a character if I'm given control over a voiced protagonist.
I don'r necessarily prefer one method over the other by default, but I think some games are better for leaving the main character a blank slate and some have interesting leads.
The problem for me is when a game ends up in the middle. I often had trouble with the way Shepard said things in Mass Effect, because I didn't feel like any of the options expressed what I wanted to say. If Shepard was capable of doing things on his own, I wouldn't have minded, because then I have a sense of who he is and I can get invested in his choices; I make decisions with his best interest in mind instead of my own. Mass Effect 3 didn't have this problem a much as the first 2
When a voiced protagonist's every action is dictated by me, I can neither convince myself that we're the same person, because although we may agree on certain things, we behave differently, and I can't get invested personally because the character never makes any decisions of their own.
I don't have this problem in games like Red Dead: Redemption and The Witcher, because the leads in those games still make crucial decisions on their own, and they have history that's not determined by me.
Still though, I think my favorite self insert protagonist is the Exile, from Sith Lords. The Exile somehow manages to be both a character in his own right, and a blank slate.
I think The Exile works because he has a history; the game doesn't so much tell you to build a character from scratch as it asks you what kind of person would do the things The Exile did.
When we play games, we adopt a sort of openness; while it's true that we might bring over our fundamental principals or instincts into a game, we also enter with an understanding that this world is not our own, and that we've yet to grasp it's entirety.
By giving the Exile a past, Obsidian afforded me a look into the nature of the galaxy Sith Lords takes place in, whilst providing me with an evocative question to build my character with; not simply "Who are you?" but "Who WERE you?".
This also brings up an oft overlooked issue; how much do people change? How different is the Exile than he was when he made his decision years ago? Can we even be said to be the same person as we were long ago, and if so, how can we make decisions about for ourselves if we don't know who will have to live with them one day?
I kinda digressed, huh? (I really like KOTOR II). In conclusion; I do self insert, but I'm not sure I have the same understanding of the term as most people.