Excellent answers actually – and yes, often early on in locked-room mysteries, the killer *is* assumed to be a supernatural being by superstitious police or towns people, etc.
They were first written in the 19th century when belief in ghosts was a LOT more common than now, and slueths like Sherlock Holmes were supposed to show the power of Reason, etc.
and sometimes the answer turned out to be supernatural – or at least unresolved. It’s what makes them fun.