Yes, they could have what we have. True democracy where the King of USA is almost always extremely rich and nominated by one or two ruling parties (choice, yay!) and the next Prime Minister of the UK will be selected by less than 100,000 geriatric Conservative Party members. Go democracy!

The whole point of banishing him to the Nights Watch was to appease the Unsullied and Dothraki. They knew that his real fate was to be the King Beyond the Wall - hence Tormund and the free folk being there for him.