I'd say the greatest insight that I've had from writing 1,000 words every single day for nearly the past year has been that simply writing 1,000 words every single day is not enough to foster real improvement. The habit definitely helps you overcome the initial resistance that you might feel towards getting started, and if you're not already good at typing or transferring thoughts in your head into words on the screen, I'm sure it helps with that too, but there comes a point at which, if you actually want to continue growing and becoming a better writer, you need a goal other than "write every day".
For me, the act of writing something that I intend to publish, to share with others, forces me to work on the writing, to tweak it, to think about how it can be made better, to question its clarity, to question the value of what I'm sharing. If what I'm intending to share contains a story, then knowing that it's going to be shared forces me to work on storycraft, to think about how someone else is going to interpret what I wrote. None of that happens naturally when you write privately, when your only goal is to see the word counter pass 1,000.
I've found that the greatest advancements in my own writing have come when I was blogging regularly (comparing posts from one year to another makes this very obvious). Whenever I've stopped blogging regularly for long periods of time, I find that my writing stops improving, even if the overall amount of writing I'm doing on a regular basis doesn't change that much (e.g., Slack messages, comments like these, etc.).
I'm not saying that you cannot improve as a writer when you write privately, just that improvement requires working toward specific goals that you know will challenge you to improve. Write a haiku. Write a short story. Look up from your laptop, find an object, and then try to write 1,000 words describing that object in as fine detail as possible. Do the same thing with an emotion that you've felt. And if you can, share what you write. Even if others don't give you feedback, the very knowledge that somebody, somewhere, will likely be judging your writing will cause you to subconsciously work a little harder to write better, to rewrite and to edit (which is the work that actually produces good writing).