Board Thread:Naruto Discussions/@comment-26993711-20170603214204/@comment-734582-20170608062655

Kakashisologod1 wrote: Hidden cloud was the leader in the 4th war alliance duo to never using akatsuki. Yet they also were the strongest, both in village and Kage.

It's a bit of a running theme that justice equals power. The Hokage that founded an era and instilled a sense of purpose into hundreds of thousands was also the strongest, whereas the people who were wrong tended to be strong, yet always weaker.

You could argue endlessly whether in Naruto Might Makes Right or Right Makes Might, but it makes sense that in the fighting-oriented world, power also means the ability to impact the world, and the people who impact the world the most (for the better) get to be (Ho)Kage.