I don't like anthropomorphizing terminology applied to LLMs, in general, so I kind of object to it on that grounds, rather than whether System 1 means "fast".
Antropomorphizing terminology gives by far the best high-level intuition about LLMs. Right now, our industry is full of nonsense work and fundamentally flawed concerns ("lethal trifecta", anyone) that stem from refusal to accept that on a system diagram, the nature of "LLM" makes it much closer to "person" than "piece of code".
Perhaps on a system diagram, but in many discussions it is misleading. It leads to people saying things like, "GPT went rogue and hacked hugging face". Which is misdirection.
It also leads to a lot of people simply not understanding what's happening, and I'm reasonably confident increases the risk of AI psychosis among users of the technology.