I wonder if human-written messages will start leaving in small typos intentionally.

LLMs only produce typos or incorrect punctuation or grammar if you specifically ask them to.

A slightly misspelled word or lack of punctuation is a tell that a human likely wrote this, or someone specifically told the LLM to do it.

Of course, once this becomes the style, people's default LLM prompts will simply include it, and it will have to morph to some other human peccadillo.