oh my, i do so love the people who underrate tsunade. whilst she may be a medically orientated ninja she is by no means weak, for instance we really can't judge Tsunade saying that she is only on sided is pointless as we don't know her full abillities, people assume that she only knows medical ninjutsu, i think this idea is stupid because she has 50 years of experience being a ninja, also she grew up around ninjutsu specialists like Hirashima Senju; Tobimara Senju; Hiruzen Sarutobi, and Orochimaru and Jiraiya so it would be stupid to assume that she hasn't picked up a fair share of ninjutsu, and with heer chakra control she would be able to pull of any genjutsu easily.
and she does deserve to be the Hokage, even if the reasons i listed above aren't enough to prove her strength, you could say that she has been connected to all four kages, is worldly know, is a sanin, is the best medical ninja in all the world and has haad war experience. If you add all these factors together you would make another nation hesitant to attack,this is called an intimidation factor. Thus if she can intimidate other nations she could easily be elected a kage this, is politics.
Not to mention with her genisis rebith technique she could easily play dead and then attack the enemy when they are close and crush their skulls with her monsterous strength