Writing as thinking
The Zeigarnik effect is where open tasks tend to occupy our short term memory until they are done. We can trick our minds to stop thinking about these open tasks by writing them down.
As opposed to thinking alone, writing allows us to distance ourselves from our ideas, in turn allowing us to assess them better ( Turn to face your beliefs, then throw rocks at them). Using written language allows for an idea to be stabilized and scrutinized clearly. In the act of writing, what in the mind may have been a large nebulous idea might end up becoming multiple more clear and concise ideas.
Writing down an idea also takes it out of our Working mental resources, freeing up those resources to be used for actually scrutinizing and developing the ideas that are now written down rather than idling in our minds.
There may be some nuance lost in the process of writing down ideas rather than keeping them in their abstract, nebulous form in the mind. For this reason, I think it’s valuable to Use intentionally ambiguous naming to avoid restricting growing or uncertain ideas).
Generally though, as memory and mental biases have such high fallibility, I see little downside (aside from Time/Effort Cost) to writing down ideas as much as possible. It is possible that writing down ideas does not erase the more abstract mental version of the idea either, and future writings or speakings can still continue to try to illumniate the more abstract mental version.