Ask Rokudaime 火影

Take the words straight out of my mouth. Hokage rarely fight. Tsunade doesn’t actually fight until something serious happen, like Pain Invasion and The World War, in which she is forced to contribute. Otherwise, Hokage would sit on their desk and worry about politics all day. You know…rules, law, taxes, economy, whatever a Hokage do.

If Tsunade contributed by giving up her medical skills to heal everybody (during the Pain invasion), Kakashi would contribute by giving strategies and making plans for his ninja to fight, since that is his best skill, analyzing. He had been a captain for ANBU at the age of 14 and was a commander of the third unit during the 4th war. On the battlefield, he is analytical and knows how to set up a strategy to win against the enemies. That’s what his strength is. Even Minato praised him for it. If Kakashi is strong but had no idea how to fight, then it would be pointless, he would just be another strong shinobi who knows how to use his power but clueless on the battlefield. That’s not the Kakashi that I want to see. 

Kakashi is just as a smart as Shikamaru (5/5 in his stats for intelligence) and is a noted expert strategist. He can lead various types of unit with ease easily recognising his comrades’ strengths and utilising them effectively, from three-man cells, to larger anbu units, and then on to an entire division in the war. He was picked for his role as commander of Division Three because of his fine tactical mind. Kakashi was also touted or recommended for the post by a number of prominent shinobi (Jiraiya, Shikaku, Gaara and the other kages), and his sharingan was never mentioned once in those conversations. Kakashi was also the one to devise the strategy that ultimately defeated Kaguya. All the strength in the world is for naught without the brain to back it up (the bijuu seem to be a good example, hence why jinchurikis were made). Finally Kakashi has the perfect temperament for politics and I think that’s most readily seen in the scene were Naruto seeks out the Raikage and is promptly admonished by A, and Kakashi talks earnestly but sincerely on Naruto’s behalf. That conversation sticks in A’s mind and leads A to agree with Gaara’s recommendation re. Kakashi.

Kakashi’s preference for teamwork is also viewed as a weakness but I think it’s the opposite (and the manga repeatedly emphasises that teamwork is better than going it alone), perhaps best seen during The Last - Mei and Onoki take on the meteors single-handedly, resulting in some hitting their villages as Mei can’t be everywhere at once and Onoki’s back gives out. Kakashi and A rely on their shinobi (Lee’s Eight Gates Team and the Kumo team’s chakra for their cannons) and suffer no damage (yes, I know, Kakashi nearly took a meteor to the face but he was saved by none other than Sasuke - a shinobi loyal to Konoha, using a variant of a jutsu that Kakashi had taught him! (good karma!))