Take european gargoyles, with an archeo-anthropologist eye. They are all over churches built during a 500-1000 year span. The most important cathedrals tend to have more gargoyles. They're the most obviously supernatural element....
What role do gargoyles play in European religion or culture? Pretty much none. There are obviously some myths and a Disney movie, but they're just not as important as you would think.
Gargoyles are really just rain spouts to protect masonry work. Obviously under different name they date back at least as far as ancient Egyptians where they were in the form of lion heads and those were copied in Ancient Greece. At some point they were converted to “grotesques” (the supernatural creatures you reference) mostly winged dragon like creatures.
The real irony is on many of the churches they lost their actual function (diverting rain water). I think that is the real cultural reference of the time, the people lost knowledge and took something that had practical function and converted it to just decorations that had no real function (except to ward off spirits...supernatural as you say).
So as you say in a vacuum it’s nearly impossible to understand certain cultural representations in art, because who knows what practical function these representations may have had in another culture predating the Egyptians, the Egyptians just copied because of supernatural reasons. That said obviously domesticated cats provided real function back then and killing snakes was a big part of that, without needing to interprete their legends and artistic depictions of the same.
Perhaps you are proving your own point by overlooking another purpose for grotesques and gargoyles - they were used as a means of attracting pagans to church.
Christianity in Europe appropriated many of the pagan rituals and beliefs - and incorporation of the symbols of the pagan religions played a part in the growth of Christianity in Europe, where paganism thrived. It was, therefore, a marketing tool as well as a rain control mechanism.