I think you are all underestimating Kuzan.
He may look lazy but he isn't stupid nor incompetent. The Straw Hats were a minor threat by then, he was aware of their heroism in Arabasta and, if I recall correctly, of Garp being Luffy's grandfather. Compare it to Jozu, who he froze to the bone the moment the pirate made a small mistake (imagine what he will do to actually evil people).
The fact that Sengoku personally appointed him says a lot about the potential of the guy. Let's remember that Sengoku was the person who knew the job and the Navy the best, lots of things from the World Government and the history of the world. He's also one of the smartest people in the world, so won't be playing stupid or emotional when choosing (and, anyways, hasn't been shown to be a soft guy, he is one of the grayest marines, so I doubt he would act by cronyism). On top of this, he was aware of Kuzan being a close admirer of Garp and his pupil, yet was confident enough he wouldn't be as absent as him. To put it simple, none of us is meant to know better than Sengoku, so if he he thought Kuzan would fit, then more than likely he would in fact fit and end of story.
On the other hand, Kuzan is actually a very active player and didn't take long before he started to move in the underworld and manage his situation with brains. That is something that many bureaucrats wouldn't even dream of achieving and I'm not sure to what extent people like Kizaru or even Sengoku would be able to "get dirty" that easily.
And I'll be honest, I personally think he will in fact be the next Fleet Admiral.