What’s the matter with paternosters? Step lively, now! 
Paternosters are awesome. There were a couple of governmental buildings in Budapest that still implemented them. Kinda freaky at first, but you get used to it.
So, how often do the elevators check for a button press? If the elevator is ascending from the 1st floor and I’m on the 3rd floor headed up, will the elevator stop for me if I press the button after it passes the 2nd floor, but before it reaches the 3rd?
Elevator controls are programmable. Door closing speed, floor-to-floor speed and prioritization are just some of the features that can be set by a technician. Doors that close too fast can hit someone who is in line to get on, even with the recoil feature. You may have noticed that elevator doors will, after the second interference with the closing function, move like molasses the third time. This is deliberate; the people who design these things make the elevator control assume that there is some sort of problem when the doors don’t close properly and slow them down to avoid injuring someone who may be passed out in the doorway (for example).