My guess is that she's as fit for leading Equestria as Celestia and Luna were when they started ruling. I think one of her stumbling stones is that she's built up what being a princess "is" in her head, and she's busy trying to be that, instead of being the kind of leader that she's already capable of being. Specifically, she shouldn't be "The Princess", she should be the "Princess of Friendship".
Ignoring the early offer of assistance in the episode is, after all, counter to a lot of things that she herself has learned, and to things she's told other ponies, as she's learned more about friendship, magic, and harmony. So if she'd just taken time to embody friendship there, she'd have quickly taken the momentary hit to princess-ly image to say "Actually, we could use some help, thank you!" early on. We wouldn't have gotten the same conflict in the episode if she'd done that, though, so she's still gotta learn how to embody Friendship in this particular venue. That'll come with practice.