I don't think those "door close" buttons in an elevator actually do anything. It wouldn't surprise me if you looked behind the control panel and found out that they aren't even hooked up.
Maybe the elevator people just put them there to make you feel better. Maybe it's something even more nefarious. Maybe, just maybe, some engineer had a twisted sense of humor and rigged it so that when you push the "door close" button, it actually takes longer for them to close. It certainly feels that way when I push it!
Making a feeble old lady have to take the stairs has never been more difficult. Will the aggravations never end? ;-)