I was never asked to close the bin. I think its an FCC rule to have the Flight Attendants secure the bins during their final checks for pushback. Lets say a passenger did not firmly secure the bin and the items fell out and I got hurt who would be responsible?

Just like they never ask passengers to pour coffee its done by the Flight attendants. WE pay for their services and part of it is closing the bins.

This flight attendant could get into some trouble if she did not make sure the bins were secure. Furthermore it would add time for the flight attendant to double check the bins were secure.

I think the airline needs to install automatic bins that are controlled from the cockpit which close and lock until the plane reaches 10,000 feet or in rough air. An there would be a 30 second delay after the bin was opened and it would close automatically and secure itself. To unlock you just press the open button.