Look, she's the best healer there is. She's simply no warrior type, really. Gai could defeat her only after going 7 gates, since that's when he can use his only, as of now, long-distance technique.
But Kakashi knows a bunch of long-distanced jutsu, he just has to be careful not to engage her in taijutsu.
Let's start with the fact that Kakashi doesn't want to be a kage and most likely never did.
Tsunade is a kage because she was suggested by Jirayia, who said that she is the perfect choice, considering she's a Sannin.
No one thought of Tsunade being kage until Jirayia suggested that.
