Sasuke's statement may look sudden but It did the job- think about the reason what it did-
It broke ice and saved him long speech about what he wants. The panel showing Itachi's words to Naruto was the explanation. It is not about the position of hokage. It's the acknowledgement that he is there and is going to try to make a place for himself among them again.
The current situation of both guys is somewhat opposite than the start of the manga- Naruto needed to make his place then and now It's Sasuke who will have to prove himself and he is willing to work for it.
Whether he becomes one or not is secondary. Just my two cents.
I actually think it was the opposite. Naruto's reflection on Itachi's words showed him that Sasuke was not fit to become Hokage because he isn't acknowledged by everyone. That's why he told him that he will be the one to become Hokage, not Sasuke.
Of course, Sasuke said that he didn't care what everyone thought, but he was going to become Hokage anyway and right the wrongs of the Uchiha. Sasuke will become Hokage by force, not by acknowledgement, and that will lead to him and Naruto fighting.