I'd say "judgment" rather than the significantly more loaded "whims", but you're right, the policy still relies on a human arbiter.
A codified system is bound to introduce problems: 'You get one bathroom break during class per week, and you've used yours, but this is an emergency? Sorry, I trust you, but the system says I have to give you detention if you go.'
My point was that the problem was with GP's specific (though perhaps commonplace) school culture/teachers, not the general idea of requiring permission.
