This is an unserious thread meant for fun and laughter because that's how I feel.
It seems that in every team a hokage comes out of, someone else in that squad feels they have a need to become Hokage too, at any costs. I cite:
Leader of Root (don't remember his name and don't even know if he was in the third's three man team so i'm just assuming)
Pein and Konan (Jiraiya gave too much attention to Minato which pushed Pein and Konan to band together to take their revenge on the world)
Orochimaru (third doesn't name a successor, Tsunade become Hokage though, however since he wasn't named, he knew one of the other Sannin would be Hokage since they are the strongest in/from Konoha)
Sasuke (you won't see it now, but when Naruto eventually becomes hokage, Sasuke will get jealous and not lack hatred in trying to oust him)
I guess the first and second hokages are exceptions to this violent cycle. I believe Konoha will never realize how many of their enemies they train and will continue to go through this vicious cycle until time ceases. Or, maybe Shikamaru will figure it out, but he's lazy after all.
Please post other wierd theories like Jiraiya pulling a James Bond on Konan and them running away together.
edit: both the first and second hokages were bros and technically their own squad and no fighting occured because both got to be hokage