Strictly speaking, Konoha's last legitimate Hokage was not the Third Hokage currently seated at the head of the conference room, but Danzo, who had already defected.
Danzo was the acting Hokage truly recognized by both the village and the Land of Fire's daimyo, the Third Hokage's official and legitimate successor.
Of course, after Danzo secretly conducted the Bloodline Fusion Ritual, causing over a thousand Konoha shinobi casualties before defecting, the village naturally stripped him of his status as acting Hokage.
So, strictly speaking, the position of Hokage in present-day Konoha was actually vacant.
Everyone had tacitly accepted the Third Hokage's assumption of Danzo's duties only because, after Danzo's defection, the entire village had been thrown into panic and urgently needed a seasoned, prestigious powerhouse to step forward and stabilize morale.
Now, Uchiha Fugaku had used this as grounds to demand a formal election for the Fifth Hokage at the high-level meeting. Legally speaking, there was no refuting it.
After only a brief pause for thought, the Third Hokage, seated at the head of the table, nodded. "That's right. The village should indeed formally elect the Fifth Hokage."
Utatane Koharu's expression changed. "Hiruzen, how could you..."
The Third Hokage first gestured for Utatane Koharu to remain calm, then addressed everyone with a composed expression. "I only temporarily assumed the position of Hokage because circumstances forced it upon us. Now that the situation has stabilized, it is time to elect the Fifth Hokage."
The Third Hokage truly did not wish to hand the Hokage position over to the Uchiha Clan, but he was even less willing to undermine the village's rules.
Those rules were what ensured the Hokage Faction could be passed down continuously. If he himself broke them, others would be able to follow his example in the future.
Utatane Koharu