Like I said, you aren't supposed to feel connected to the character. You ARE the character. Playing Splinter Cell, you aren't Sam Fisher. You're playing AS Sam Fisher, because he's his own character with his own story and motivations. In the first-person immersion games, the character is a blank slate because YOU are the character. The character is just an anolog to put YOURSELF into the game, where the choices made and the emotions felt are yours, the player's, not the character's.
You're talking about being immersed in a story from an outside perspective. I'm talking about literally being in and part of the story.
But you are never in a game, you are always having a controller, and if you are in a game will you be ordered around, not have an opinion, and never act according to your will ?!, I don't see how I am in any game and be just blank, I feel connected to a character, and that's only when I feel I am that character.
As for Sam Fisher believe it or not to a certain degree you shape him, in Chaos Theory for example you can either save the 2 pilots from the blast radius or just leave them, that is you deciding what to do, Sam's actions is a reflection of your own self, in FPS blank character ........., well you never have such choice, that's why Splinter Cell ends up being more engaging to me than any other game.
I enjoy FPS games like Resistance series or Killzone series where there are real characters, as opposed to Call of Duty, Crysis or Battlefield, where I am so disconnected from the character, the story actually begins to not matter since it doesn't affect the character at all, there is no input from you, you just play, that's not immersion in my opinion, whenever I see a character that actually have a character I imagine myself as him, I don't do so with blank characters.
I may show my point better but it depends, did you play Medal of Honor 2010 ?!