Just composing in the head is a nice first step, but merely thinking about something makes it easy to gloss over flaws in your thinking that you have to face when wrting something down (if you do non-stream-of-consciousness writing).

On the other hand you have to think about things only tangentially related to the actual problem you are writing about like style, grammer and finding the right words.

So there are advantages and disadvantages to actually writing stuff down.