What you're describing though is that individual source of content tends to sound like itself. That isn't a problem so much as what we tend to want and expect.
When we say AI sounds same-ish we mean all sources of content can sound the same - fiction and non-fiction, news articles and blog posts, marketing pitches and ai drafted personal messages, all sound kinda the same. That is a different situation, and that's before you get to "and that one sound is LLMish".
When we say AI sounds same-ish we mean all sources of content can sound the same - fiction and non-fiction, news articles and blog posts, marketing pitches and ai drafted personal messages, all sound kinda the same. That is a different situation, and that's before you get to "and that one sound is LLMish".