Proposition: The GM's primary duty or role is to decide whether or not something is possible.
Everything else is optional and accounts for various playstyles. The GM doesn't have to come up with challenges; you could use a monster player, or an elaborate random menace generator, or secret ballot. The GM doesn't have to be the only arbiter of rules. The GM doesn't even have to handle dice decisions. But deciding whether a roll is possible, and then deciding whether it's necessary, is the core GM duty.