My only concern is that the remaining pilot falls asleep due to boredom or needs to go to the bathroom.
You have just contradicted your own statement. Thats at least two reasons why you need two pilots in the flight deck during all stages of flight.
Having less crew on long haul flights also means that each pilot will get more opportunities to take-off and land, which are the critical parts of the flight.
So instead of doing 10 take-off and landings a year they get to do 12? Not sure that is going to substantially enhance the flying skills of long haul pilots.