It’s ok to use it as inspiration, but using the term comes with psychological baggage in an industry that already abuses anthropomorphism. Give it an informative name
System 1 is quite informative about what it's for. It means it's a system designed for bounded time quick classification, vs. agentic unbounded or slow thinking with scratchpads and tools.
Does it inject thoughts into system 2 without system 2 knowing about it? Does it have instinctive social skills? Can it do instinctive arithmetic? The list goes on, there’s a nice book about it…
Were people getting their pants tied up in knots like this over names like daemon programs (a term that carries "baggage" of its own) and installation wizards (which, to my knowledge, do not actually invoke in the arcane)?