I think Kishi is trying to find a reason to have Sasuke and Naruto fight without messing up Sasuke's new alliance with the good side again. Maybe they'll end up fighting for the rights to the Hokage title, but Naruto will really be fighting to make Sasuke realize the true meaning of being Hokage like Itachi told him. Picture this
War is over
Naruto and Sasuke have epic talk no jutsu moment about the village and becoming Hokage
Sasuke says he wants to change the village and become Hokage so everyone will acknowledge him and he doesn't care what people think about him
Naruto says that's not what being Hokage is about and he'll never become Hokage like that
Sasuke challenges him to a fight to see who deserves the title more
Naruto proves to be stronger and wins
Sasuke asks what makes you so strong?
Naruto says something like "the bond and acknowledgement of our friends. That's what gives me the strength to overcome any obstacle. The one who is acknowledged by everyone becomes Hokage, not the other way around. I learned that from Itachi"
Sasuke has a revelation and finally understands the true meaning of being Hokage and friendship, thus devoting his life to gaining the acknowledgement of his comrades, and becomes Naruto's advisor when he becomes Hokage, and then becomes Hokage after Naruto