Because there is no "Official" Shield, so no official policy to challenge him with. Shield was a multinational organization with their authority granted to them by the World Security Council, probably through interlocking treaties. In the aftermath the WSC disbanded Shield, cut its funding sources, stripped its authority to operate in sponsor government territories (including the US), and so officially it ceased to exist.
Neither Coulson or Gonzales have an "official" claim to the name. Coulson's authority purely comes from what he inspires in his people and that he is Fury's protege and holds the toolbox. Gonzales's authority comes what he inspires from his people and his command of the aircraft Carrier Iliad (not helicarrier, at least not yet). And both of them maintain their respective commands only because General Talbot hasn't come through, confiscated their equipment, and disbanded them.
To follow "Official Procedure" to replace Fury as head of Shield, candidates would be presented to the WSC and they would appoint Fury's replacement. However most of the members of the WSC are dead at the end of Winter Soldier. The replacement council members appointed by the sponsor nations either approved or ordered that Shield was disbanded. So to "officially" replace Fury, the council, who has labeled Shield a terrorist organization and disbanded it, would have to decide between Gonzales or Coulson. At this point they would just be arrested and their Shield assets would be seized to be used by whatever replaces Shield.
