> Saying “AI writing lacks character” is like saying typewriters can’t produce an authentic letter, only a handwritten letter can be authentic.
You're making a flawed comparison there. It boils down to style.
Style is a personal thing, it comes from your word-choices and the rhythm of your writing, which results from how you feel, your education and interests, what audience you're trying to reach, your lived experience, whether there's a 3 year old trying to show you that he can eat a bug.
Now, of course, a hand-written letter has a greater expressive capacity: you have paper choices, ink or pencil or crayon, your hand-writing either natural or emphasised. A type-writer can't capture that, but the words you type are still a reflection of you.
AI makes few of these considerations, and is unable to convincingly emulate them.
Strongly recommend you read Don Watson's Death Sentence: The Decay of Public Language for a good comparison of the bland paste we get fed by institutions (and AI) and robust writing from the heart meant to persuade or reflect feelings.