Any good editor or writer will tell you the following: There are two lines of narrative inside of a good novel. Short stories, particularly pulp sword and sorcery type stories, often only have one of these lines. The two lines are the external story and the internal story.
In long form story telling, like a novel, you must have both or your story is flat. The protagonist is doing things to achieve an external desire. They want the money, they want the girl, they want the boy, they want to get to Nome with the vaccine, they want to get the ring to Mount Doom so they can throw it in.
Whatever the character is doing is leading the character toward a the final achievement (or failure to achieve) the desired outcome. This is the external story.
The internal line of the narrative is how the experience of moving toward the external desire changes the person. Often, there is a dissonance between who the character wants to be and who the character is at the beginning of the story. In order to achieve their external goal they may have to change how they think or what they believe, first.
Bilbo Baggins at the beginning of The Hobbit takes after his Baggins father. He’s the very typical hobbit. The Took side of him is separated from the Baggins side. As he goes through his various adventures, the two parts of his personality are integrated and he becomes a complete person. This is the internal line of the story and we, as the audience, get to observe it.
Characters in a tabletop roleplaying game can change internally. In my experience, that only happens if you run a long term campaign.
Short term or one shot games are more like a comic book or pulp short story. The character doesn’t have an internal story arc. They will have a dilemma but the character is set in their ways. Conan is never going to change his mind about civilization or the practical application of a sword to his problems.
Conan is the way he is and does not change. He might learn something but it doesn’t change what he wants or how he goes about getting it.
Internal story arc is one of those things that tabletop roleplaying games don’t do well. A mechanic that shows a mental shift in a character will lack the emotional punch of a story. A character’s inner thought is something you are not typically concerned about in a game.
Call of Cthulhu has mechanisms to mark the growing insanity of a character as they learn more about the mythos. This has been a mechanism that gets a lot of conversation and tinkering. It’s hard to show a change in a character emotionally with a game.
If an emotional shift is going to happen, it’s likely within the player and how they play the character. That takes time. This is why I have only seen a shift in a characters during long term campaigns.
The players learn who the characters are from decisions they make in the moment, at the table. Through decisions the players make, the character is revealed. Eventually, the player understands the character. At some point, there may be a shift. The character may decide they want something and determine the only way to get it is by changing how they act or what they believe.
The internal story happens to that character but the only person who really gets to experience the change is that player.
I think that each player having their own personal emotional experience of a the game unique to their character is beautiful. It’s hard to make that available to everyone at the table the way an author can inform readers about a character’s thoughts and feelings over the length of a novel.