They probably couldn't do any more than they could do when the manually operated elevator got stuck between floors.

I think the real reason that elevator operators stayed on for a period of time is the same reason that some older people sometimes reject new technology, such as smartphones or in-home digital assistants, even when it ostensibly makes a lot of things easier. The same thing probably happened with push-button elevators. People didn't want to have to think about pushing buttons when they were used to just stepping into the elevator and telling the operator what floor they needed, or more likely the operator already knew.