That's the problem. Where did it indicate that he should be or worthy to be a Hokage? Tsunade was in tired state back in Kage Summit, so it's understandable to get a good candidate. Here, what's the reason? Just to get more ways for Sasuke to get scout free? Because that's what it seems like and it only makes it more biased and controversial. I mean out of nowhere, Kakashi should be Hokage topic came from Obito. Why? Because...reasons.
Tsunade has stated once or twice that Kakashi will become Hokage if anything happens to her, and the 5 Kages voted for him unanimously. It was done out of necessity, sure, but the Raikage was willing to vote for him because Kakashi was willing to put diplomacy at the table at a tense political climate. The big guy's rash, but he is reasonable if he gets talked down. That's what he respected from Kakashi, at the very least.
What I'm trying to say is, Kakashi had the recognition of just about every shinobi all over. He had the leadership skills, abilities and wisdom to become Hokage. The whole point of Kakashi becoming Hokage was for him to stop running away from himself. Itachi himself said, you don't get acknowledged because you're Hokage, it's because you're acknowledged that you become Hokage. This might have been the true point of Itachi's speech. Except the twist with Kakashi's case is that he also needs to acknowledge himself too.
