Humans just aren't very good at understanding their own motivations. Marketers know this implicitly. Almost nobody believes "I drink Coca-Cola because billions of dollars of advertising have conditioned me to associate Coke with positive feelings on a subconscious level", even if they would recognise that as a completely plausible explanation for why other people like Coca-Cola.

> unless it's a self-insert?

In the case of LLMs, there is zero reason to believe the LLM is capable of doing that--and a bunch of reasons against it.

However the concept spreads because some humans are deliberately fostering the illusion.