I don't know of any system that is more responsive the more rapidly you give it identical input outside of, say, games that are specifically designed to that end (the faster you mash the 'A' button, the faster your racecar will go!).
But I think it is learned behavior. Suppose for a moment that your name is Clodor and you're in an elevator. You press the 'close' button. The button lights up, but nothing happens. Huh. So you press it again. And again, nothing happens. Then you press it a third time and well what do you know! The doors closed. Third time must've been the charm, right? So, the next day you do it again. 'Close the door'. 'Close the door'. 'Close the door'. Door closes. Yup. Must be your repeated input. Then the next day, used to this odd design choice these elevator designers went with, you press the button more rapidly than before. Except now it takes four times. Huh. It must not have a set number of inputs before it does what I want, it must just be a case of "The more I press it, the more likely it will be that it will respond".
This is called Confirmation Bias and it plagues us humans. We assume the elevators work this way and we do tests to confirm it, never trying to prove ourselves wrong (being patient, in this example). Apply this to our interactions with inputs in general, and, well, you get the idea.
Note: The confirmation bias is not the culprit here. The real way to solve this problem would be to either make the elevator doors close immediately or to provide some clear-cut message that says in no uncertain terms "We hear you, brah. We be closing the doors in short order", possibly even a recording that says something like that (preferably, in my opinion, exactly that). I know that those buttons on elevators tend to light up to indicate they got the message, but apparently humans don't get the message that the elevator got the message, so we may need something a bit more blatant.
Also, though elevators are used in this answer, this really applies to any interaction where the action requested does not happen immediately after the request. How many times have we clicked "OK" before that dialog box finally went away, even when the button made the pop-in pop-out animation? How much better would it be if we got a spinner at that moment to at least let us know it was working on it?
But as far as elevators go, I don't really see this "problem" being addressed by the industry, as it's not really a "problem" whether you press the button once or twenty times.