This question applies to most people, and it certainly applies to me: does it make sense to write without an audience?
It does.
One of my favorite books is Pragmatic thinking and learning by Andy Hunt. It's a book about how our brains work, which is a subject I find fascinating. A core concept it develops is how our brains operate in two modes: the linear and logical (L-mode); and the intuitive, holistic, and magically powerful (R-mode)¹:
R-mode is critical for intuition, problem-solving, and creativity. L-mode gives you the power to work through the details and make things happen.
You need to leverage both modes in any creative endeavor, which is easier said than done. L-mode is deliberate: it happens when you focus and concentrate. R-mode, however, can't be commanded, only invited.
R-mode triggers when you disconnect your train of thought (e.g: taking a shower or walking), but also when you write! Because it's so powerful, it might happen that your R-mode already knows the answer to some hard problem you are working on, you just don't know it yet. Believe it or not, writing can let you harvest those answers. Are you skeptical? How often have you figured out the answer by writing down a question for a colleague? No magic here; this is science.
I often do this when I am tackling a complex problem. First, I study and analyze. I deliberately consume a lot of information. And second, I try to write down a high-level description of a possible solution for myself. There is no need to draw anything or use fancy notations, just describe the solution with good old words and paragraphs. You can discard the resulting text; the value resides in forcing you to switch to L-mode, hopefully inviting your R-mode to connect the dots from all the information you have ingested.
In addition to being a thinking tool, writing can do wonders for your well-being. When you write your thoughts down, they somehow abandon your mind, so writing about things that bother you is a great idea. Again, this is not magic: it's impossible to write without exercising your L-mode, and because this mode is logical, this normally translates into adding clarity to fuzzy concerns you carry around. What you identify as clearing your mind is just the fuzziness disappearing.
I am entirely ignorant of this matter, but I am not surprised to find many references to how writing can be therapeutical. Some of my favorite pieces I've written originated in something that was really bugging me. I love them because they represent a before and after for me, independently of whether they resonate with others. Before, something was cloudy; after, something was clear; everything happened between my two ears.
So, good for your thinking and good for your well-being. Write. Even if nobody is reading.
¹ Thinking, Fast and Slow is a better-known book on this very same subject. I found it very dense and academic, though.
¹ Thinking, Fast and Slow is a better-known book on this very same subject. I found it very dense and academic, though.