Writing changes your thoughts from abstract to concrete - and once a thought is "out of your head" on paper, it becomes an entity that you can perform additional thought operations on (which you can then write down...etc.).
Analog writing also leaves visual evidence of your thought process across a page. Most digital writing tools allow you to make the thought process disappear completely as you work. Having evidence of your thought process allows you to evaluate your thought process. Very important in any kind of problem solving exercise.
As a child, I found that writing down a thought that bothered me made it go away and freed my brain up to do kid stuff.