Star Wars politics often seem to be an argument about who has the right to wield power. Under the original Republic, power was seen as being the right of those born to wield it, i.e. hereditary rulers and those born with Force powers. Under the Empire, power belonged to whomever had the strength/ambition, etc. to seize and maintain it. Only a small group of people seemed to honestly believe that power should be vested within the people. Even Padme, the champion of democracy, dismisses this idea. When the people wanted to make her monarch for life, she refused because, as she said, the average person knows what they want, but not what is best for them.

Leia seemed to very much subscribe to this philosophy. As a woman born to nobility and trained to rule, only she can lead effectively. Only she can be trusted with power. She should be chancellor and she should have her own private army, because only she can be trusted to use them responsibly. And yeah, she's the hero, so the narrative more or less supports her on this without really questioning it, but it sure is an interesting position to take.