"out of sight out of mind" - In other words, writing it down allows you to let go and relax.
Also, the written word can be very powerful for a number of reasons. I've noticed, that when something comes up in a mind sweep, or weekly review which I have resistance towards, I hesitate even to write it down, as that is the first step towards making a committment.
Thoughts are fleeting, and if there's one that represents a responsibilty you don't feel like tackling, you can quickly replace it with another thought.
If you find that writing it all down is as stressful as not, then there has to be a good reason - resistance? procrastination?
My journey into GTD has made me realize that all those years of procrastination existed for a reason - because I was afraid of my own clarity and creativity - now that my decks (inbox, email, etc) are cleared on a very regular basis, I feel like the proverbial artist facing the blank canvas - alternately terrified and exhilirated - I can do anything I choose now that I've quieted the noise and the backlog, so what will I do, and thereby become responsible to?
I used procrastination as a means of avoiding repsonsibility - "oh, I can't take on that project just now, because I've got all this 'stuff' in my face to deal with first....."
David Allen's analogy of martial arts is quite appropriate, as one is working on layers of themselves, as they master successive "belts" of efficiency and clarity.