I think that the close doors button in an elevator does very little. If it works, it saves the person two seconds of their time. If time matters this much to people, why do people stand still on escalators, instead of walking up the steps?
Having the button there can lead to people accidentally pressing the open doors button, in their rush to find the right button, which delays them even further. If the close doors button doesn't do anything, then this means it can only cause delays, and the absence of the button can solve this problem of behaviour that negatively affects oneself.
Not having the button wouldn't lead to people feeling trapped (only the opposite button would do that). Furthermore, I think a small delay before the doors close is advantageous to people who want to get into the elevator at the last minute, so the absence of the button can improve behaviour that negatively affects others.