Perhaps larping was the wrong term, but it does not really matter. And it is not only about immersion either. You can think of it as part of a puzzle that you have to solve. Using an automap takes away that element of the game from you, kinda like a walkthrough. It will just be a different experience then. I disagree that it requires no skill or thought as you have to be very careful and oberservant.
See, my point was that it is not so much about the end result but that the drawing itself is fun. And since its fun and requires more attention than you think it does not feel as disconnected as you describe, like some kind of distraction that interrupts the actual game every few steps. It is an integral part of your playing experience. It is part of the gameplay (even if it does not happen on the screen).
The automap is not the same exact map. It is a map provided to me by the computer.
Perhaps this is a shitty analogy but you could think of it as the difference between exploring on your own or using a quest compass. I think it might be hard for someone to explain why exploring can be more fun to someone who is used to the quest compass pointing him in every direction. Finding your way there on your own may seem to be pointless and tedious when the game could just direct you and the end result is exactly the same - you end up at your goal. But of course it is a different experience altogether.
