Writing is the gym for the brain. It will give you a lot of clarity on your thoughts and also improve how you speak. Your mind will be enhanced and it will affect positively all the aspects of your life.
Everybody writes, but very few do it deliberately. Most of the people, just write. They rarely even think about what they wrote. You will sound smarter. Not because of choice of words, but because you will begin to think clearly.
In the first three decades of my life. My schooling was second-rate and I've started to learn english quite late. Both my reading and writing skills were absolutely inferior to kids with a privileged background. My literacy as a kid was close to zero. My main focus was math, code and video games.
Then, having progressed in life mostly because of my technical skills and hard work, at some point I've felt my career had stalled. All my peers came from a much richer background than I and have studied in much better schools and I've started to dig into what could take me to the next level and to compete side-by-side with them.
One thing I've noticed is that I've never had a writing class before. Never. Just a few activities that one could count in one of their hands during my whole school and university life.
I've started then to write down my thoughts, then think and write. Practicing different exercises. Reading more and paying attention to other writers, to their cadence and style.
Inevitably my writing started to improve. I haven't have focused much on grammar so far and will certainly do at a later stage, as I feel there is still progress to be made in organising my thoughts.
If it interests you, try it. Feel free to send me an email if you have trouble to find time or what to write about, I can try to help you out. Let's progress together.