Just because Minato is stronger than her, doesn't mean she doesn't deserve to be a Hokage... That's an extremely 1-dimensional way of thinking. What you fail to realize is that, in the Pein Arc, Tsunade's efforts weren't about fighting, it was about protecting the village and keeping as many people alive as she could - Which she managed to do, however it was completely overshadowed by Nagato reviving them.
Tsunade never has and never will be a front line fighter, but that doesn't mean she doesn't deserve to be the Hokage. You fail to put any reason behind any of your arguments aside from "Well this Shinobi can beat her so she doesn't deserve to be the Hokage." but what you fail to realize is that a Kage has to be more than just a fighter... Heck, they don't even have to be fighters.
Naruto is obviously stronger than Tsunade, but he is in no way, shape or form ready for the title of Hokage because he's still young, immature, rash, argumentative and obviously wouldn't be able to run a village. What you also fail to realize is that Tsunade took the job for the village's sake, they had no one else to turn to, so they went to her... Why? Because Hiruzen had just died and a number of Shinobi were killed.. Jiraiya declined the position of Hokage meaning the only one left was Tsunade.
You're going to have to come with more of an argument other than "She'll be killed by this shinobi meaning she doesn't deserve to be the Hokage." In case you're forgetting she has a technique that quite literally makes her almost invincible for a set time period and she has the strength to quite literally kill anyone with a few hits. What she lacks in her fighting ability she makes up for with experience and knowledge.