Symbols, devices, etc all can gain real lasting meaning after it's left the writer's workshop. In IMO a fairly predominant school of thought in the offline world, artistic intent functionally doesn't matter outside of the conscious decision to publish a work, whether it be on twitter or in a DIY zine or in a book. As to the purpose or lack thereof, in most skilled writers this only somewhat determines how the symbols in the work are interpreted. In less skilled writers, they have no control over it at all. Which is to say, the "deeper meaning" behind a works' shorthand to describe its themes, or imagery it uses with no further intent, is entirely dependent on how the audience perceives it. That's the lasting legacy. Not the thoughts you had or didn't have while making a piece, not even the interviews where you attempt to sway the public into a certain school of thought about your piece. Just what the audience largely thinks and says.
With that said, symbols having or not having a purpose in the story doesn't matter as much as how we, the audience, perceive it. If even one person in the audience thinks it's that deep, it is that deep, because that's the legacy that will endure. I can't tell you how much personal significance one can extrapolate from, say, corny anime meant to sell toys, or how much an anti-war work can be used to sell war to people. This happens all the time. Analysis is largely meant to explore what can be, not what should be nor what was intended to be, read of a work. You can do that with just about anything.