(2) won't overshoot---i.e., won't reach the desired state so quickly that the system can't turn off the response in time. These seem to be what were missing with your sailing students.

But that's a a result of the high responsiveness of the furnace vs. the low responsiveness of the boat. You couldn't blindly let a thermostat control a boat or a missle, you would have to tune it. It some situations it might need to turn itself back off before it's input (heading) has noticeably changed.