The essay my 8 year old can currently write in scribbly handwriting certainly won't compete with the essay a classmate "writes" using ChatGPT. But the facade is paper thin and ever so short lived. Seeing how much better my kids write now, vs 2 years ago, proves how much they're learning and the incredible power of practice. Someone relying on such a serious crutch will be left behind. I guarantee it.
Unless there's some dystopian future where every aspect and communication in our lives are managed and filtered by some kind of AI middle layer. I doubt it.
Tech advancements always lead to this struggle, but it's rarely as stark as you might think. My kids are still learning cursive in school, though I can't imagine when they'll ever use it.