The pilots are definitely not "mostly asleep" on long flights. There will be two qualified pilots monitoring the aircraft at all times during the flight (with the possible exception of one stepping out for a moment to use the restroom during cruise). Long haul flights will carry relief crew, 3 or even 4 pilots total, so they can take shifts flying the aircraft.

Being asleep in the cockpit is a good way to quickly end your flying career.

When you're aloft, you are safe unless the plane is depressurized or on fire. The key safety feature in aviation is the manner in which the plane returns to the earth. This is a job for humans to manage.

Some pilots stop paying attention on long, boring stretches where the autopilot is fully capable of following a vector and an altitude. However, if there's an alarm due to control issue or other emergency, the human is alerted and would take over amyway. That's why it's called an alarm. I don't mean to imply that I support this behavior, but it is an understandable human factor that's a lower priority to correct than other safety factors.