I personally find just writing quite a challenge when trying to convey an idea to someone else, not everyone has the same learning style so I try as much as possible to use multiple mediums when explaining. For example: drawing pictures or saying something out loud including sound affects or gesticulating. So, while I agree with your point, I think that additional forms of explaining are equally as invaluable
Explaining something you think to another person sets a much higher standard than convincing yourself. You have to translate from your own brain-speak. You also must explain using concepts the other party understands. It also brings online your "convincing other people" modules, which are pretty powerful. [1]
Writing stuff down also means there's a record. Writing can stabilise your attention. It can bring you back & let you loop over parts, note diversions and pursue multiple lines of inquiry. It's extra working memory, that stuffs gold. [2]
If you're just starting out with writing things, try not to judge what you're written too harshly.
Experiment:
Set a timer for 5 minutes, pick a person in your life, now explain something to them you'd think would be useful for them. Don’t force it. Sit. intend for your writing to explain. Notice when and where you get stuck. Mull over it. Discover anything?
When you write down your thoughts, you can see them from the outside. You can bring your verification modules online. You can recognise good writing, far easier than produce it. [3]
Notes
[1] I'm reminded of how if an abstract logic puzzle is reframed in terms of other people's dishonesty subject's accuracy jumps like crazy. "the other monkey might be cheating" is the native architecture.
[2] Use a whiteboard to think better.
[3] I've heard artists call this "the gap". The space between your ability to produce and your ability to recognise good art. Also: Babble & Prune
Why Programming is a Good Medium for Expressing Poorly Understood and Sloppily Formulated Ideas - GJ Sussman
“I write because I don't know what I think until I read what I say.” ― Flannery O'Connor