Except that there are such things as speech writers, whose job is literally to write prose in the voice of the person who’s going to read it.
And there are countless other jobs out there where people are the “voice” of another party. From those who manage social media presence, to PR firms, to copyrighters, all who put statements out on others behalf.
There was already an industry of professionals whose job it was to have others write things on our behalf, and that existed long before LLMs were a thing. What LLMs did was make that that service available much more cheaply.
Speech writers and shadow writers in general are writing on behalf of other people, but they're not writing the same thing. They can't! Usually they're writing something better, with the proper voice and authentic to the views of the person, but still not the same as what they would have written.
Speech writers do not write in the voice of someone else, they create the public image of say a president who is inarticulate and make them seem polished and articulate, if anything they lend their voice and ideas to someone else. That’s why they are hired.
And no LLMs are not producing ‘the same thing’ as a speechwriter. If you are unable to tell the difference I’d suggest doing some a lot more reading of human books. LLMs produce stultifying pablum without coherence or style.