In spite of (because of) how stupid this sounds, I think there's a million dollar idea in here if you made it sufficiently frustrating and competitive.
Perhaps pushing the button increments a number that decays exponentially. And ads fly in your face to distract you, which you need to wipe away. I'm actually serious.
I tech various programming technologies. One lecture on web session handling I showed a big red button app running on a local intranet server. The problem was it had a leaderboad in it. I completely lost the class after they got the URL. One pair even went so far as to figure out how to share their session so they could combine their clicks.
Perhaps pushing the button increments a number that decays exponentially. And ads fly in your face to distract you, which you need to wipe away. I'm actually serious.