I think the pushback was that if there's an "open door" policy it is presumed to mean "open communication with the possibility of change or at least suggestions

I think the pushback was that if there's an "open door" policy it is presumed to mean "open communication with the possibility of change or at least suggestions being heard". If the supervisor you have an "open door" to communicate with has zero flexibility in what they can do to help you then you might as well converse with one of the stock-picking robots.