Writing is thinking and can often facilitate executing tasks. It can be especially invaluable when tackling complex tasks. This is because it takes clarity of though to write well; clarity being the key to unwinding a complex issue. However, writing well can take time, requiring multiple drafts and revisions.
I believe that one doesn't actually need the perfect final draft. In most cases first draft usually provides majority of the value.
At the start of a project there are many different paths. As you start a project you might have to go about exploring each fork. This can be expensive. If you are lucky or experienced you might end up on the correct path the first time around but likely you will need to at least think about each fork as you come upon it.
Writing is a tool which allow you to explore test out the different paths very cheaply. By writing out your project plan you are eliminating many possible paths you would otherwise end up exploring.
Due to the nature of this elimination, we are reaping value even from the first draft. Since most projects are not necessarily complex, even the first draft is likely to provide value and clarity of thought. Don't let the fear or perfection stop you from taking the first step.