Yes, it has seems suspicious that very little seems to happen in reaction to pressing the "close door" button in the elevator. Most other buttons have an immediate reaction: open door, floor 3, etc., but there seems to be a definite delay in response to that one button. The idea had occurred to me that the button was just there as a balance to the "open door" button, which is a necessity.
According to Patrick Carr, who runs the Elevator Historical Society, elevators are programmed to work much the same as traffic lights on a highway. They operate faster during peak hours than they do at other times of the day. Having an operational "close door" button could throw off the programming.
The close door elevator button is frustrating, so I'm not surprised to find out that it's not connected to anything. However, I don't know why they have this button in the first place then. It seems like you could save both money and frustration simply by not creating or installing this button.
No, I did not suspect this to be the case. I always figured that if a company took the time and effort to manufacture and install a "close door" button for an elevator that it would be operational. I guess it is just there to pacify impatient people, as the door already closes quickly on its own.