Would that immersion be broken if you were able to manipulate the setting as you played - make the wind on the ridge die down, decide the tunnel led to a treasure vault, make a favourite ally appear in the ruined castle? I think for a great many people it would. Being able to manipulate the world would shatter the illusion that it exists beyond the immediate needs of the game session.
The strength of the informal method is that it maintains the control of the reality of the game world within the confines of one noggin ensuring greater coherence. Furthermore, it allows most of the benefits of the narrative meta mechanics without the player actually having to bother with such. And as a lot of people find such mechanics at odds with their enjoyment, this is rather significant. It basically lets the player to pretend that the world is objectively and independently existing 'real' place even though that really isn't the case.
I want to be immersed in my character and his/her situation.by the same token, many players feel their immersion is more aided if they can craft the story to fit the way the story is progressing in their imagination. I think some people prefer to be immersed in the setting, but others feel it more important to be immersed in the story.
This has a number of aspects to it. I don't want to have to ask someone else to tell me what my memories are. That is immersive only if I am trying to play an amnesiac (I know from the experience of having been an amnesiac). This then feeds into goal-formation for my character: to be immersed in my character, I need to form goals that are rational for my character given what s/he knows about the world s/he is part of; and I can't do that if I have to acquire all that knowledge and understanding by asking someone else.
I want to be able to declare actions that cover the full spectrum of mental and physical activity. And I find it jarring if someone else at the table has superior knowledge to mine as to what my character is thinking or doing (which, again, will be the case if I have to ask the GM all the time).