> Whether a text was written by a human or not is just a single bit of information

I doubt this models reality well at all. If I write the first paragraph, and AI writes the second; a float seems to model that better. If you choose to collapse a float into a bool, I don't think you can make useful conclusions based on that bit?

> since even the shortest text contains more information than that.

I also don't think that's how information theory and bits of information works...