Well, Ill be a ***** and say that caring for Characters you see might be hard if you not are open to care about people. Take Ratchet and Clank 1 because i recently played that.
When you get a decent part into the Game when Quark betrays your trust we see Ratchet and Clank go through Character Development, Ratchet seems non caring about the fate of the Universe vs his revenge against Quark. Clank being naive and still seeking to bring peace to the Galaxy .
Now if you subscribe to Liberalistic Philosophies you might not have strong will toward caring too much about the state of other people, as is core of those Philosophies.
Each man for himself! You might not be able to feel immersed by other people, when your brain can by use of these philosophies shut off your emotional sides. (I am talking core principles and not about todays current Liberal people, dont hate! )
This call to care about Characters can be hard to make in 3rd person games and in movies, but its easy in 1st person games, as all the elements in the game speak to you and you alone.
What you must do as a player is at some point think as if you were Ratchet or Clank, that will allow you to at least entertain the idea of their personalities.
Game Designers assume us to be Human and not non caring individuals, All games has immersion, but Quality can be debated.
Yeah, I think that pretty much sums up my comment, I am not saying you dont care about Ratchet tho

Just saying Gaming might require you to immerse yourself at some point, Gaming might not all be about receiving it all, You should work for the immersion sometimes.