I think the Dragonborn depends on the player. My Dragonborn? Absolutely. Good natured and well meaning. Highly skilled and blah blah blah. She'd be perfect to lead Skyrim. Other Dragonborns, though... do you really think the leader of the Dark Brotherhood or Thieves Guild would make a better High King than Ulfric or Elisif?
Actually, a cunning leader of the Thieves Guild would probably make a better leader than a well meaning warrior who lacks the political ability and ruthlessness needed to run a kingdom.
It's why I prefer the Tiber Septim of the Arcturian Heresy than the Talos of legend.
Well, I would imagine that leaders like Genghis Khan or Alexander the Great or Julius Caesar or Alaric the Visigoth or Harald Hadrada or ...
Anyway, I think those people would probably disagree with you. It seems to me that history has a long list of well meaning warriors who were absolutely amazing kings/emperors. I think Genghis Khan has my favorite example of a warrior ruler who knows how to get things done. Once he conquered all the lands around him he was content, his people were happy, and his family strong. He reached out to the sultan in distant lands, offering peaceful trade. He had things the sultan's people wanted and they had things his people wanted. The sultan agreed and in good faith, Genghis Khan sent a caravan of goodies, but the caravan was ransacked by one of the sultan's underlings on its way. When Genghis Khan sent an emissary to find out what happened and what the punishment was going to be to that underling, the sultan messed up the emissary's face and sent him back to the Khan. Genghis Khan, being a warrior, was insulted and decided to march to the sultan's palace pillaging and killing everything in between.
That is how a well-meaning warrior king conducts business. You reach out with diplomacy and when it doesn't go right, you kill everything in sight. Nothing underhanded or diabolical. Not wheels moving wheels moving wheels. Just some good ol' kill everything that crosses your path. I have no doubt Kodlak Whiteman would make a better king than Mercer Frey... or Brynjolf, since Mercer Frey clearly has some serious issues and Brjnjolf is a badass in his own right.
I say all this when I'm a HUGE fan of espionage stories, lol. Spy novels, movies, shows... love'em all. And I think the Thieves Guild is the closest thing to that. I could totally see a Dragonborn warrior king utilizing the Thieves Guild, though. That would be awesome.