What Was the Purpose of the Teams Time in the Fire Nation?
From a writing standpoint, Book 3: Fire should definitely been set in the Fire Nation. It's a location we haven't seen much of, and it's important for the characters to explore enemy territory and get a grasp on who exactly they're fighting this war against. It also gives us, the audience, a chance to finally see the Fire Nation and its people.
But from a story perspective, what we're given doesn't make much sense. Why would Team Avatar stay in the Fire Nation leading up to the invasion? Why wouldn't they use Appa to go around and recruit as many soldiers as they can for the invasion? Hakoda and his warriors do this, but wouldn't it be faster if the gang helped? They know most of the people recruited already, and they could have hidden Aang so that word didn't spread about his survival. They could have recruited more than what we're shown in canon.
Wouldn't this have been more useful than enrolling in a Fire Nation school?
It would have been safer too, considering Aang IS caught at one point
And then we have Sokka who maintains a strict schedule. But for what purpose?
What are they working towards that requires such dedication to this schedule? Hakoda and his men are able to reach The Black Cliffs on time, along with the others. And they don't have a sky bison.
Well, the original Avatar Bible gives something of an answer at least
Zuko's role in season 2 is only mentioned twice:
So Appa was meant to be missing much earlier, and for much longer. This would mean that Aang NEEDS to be close to the Fire Lord on the Day of Black Sun, regardless of the invading forces ability to help. Staying in proximity to the capital prior to the eclipse makes sense, so lingering in Fire Nation territory would be important.
But then we get this tidbit about the GAang's other reason for being in the Fire Nation prior to the invasion:
Obviously, so much changed from the original conception of the show. The Fire Nation is not a 'barren land full of active volcanoes' and Zuko's Season 2 story line, living amongst Earth Kingdom commoners, was going to be saved for Season 3 to be the Fire Nation commoners.
But most importantly, Aang, Katara, Sokka and Toph (male version), were searching for Aang's firebending master.
And I really wish they stuck with that concept in the first half of canon season 3.
I wish they put feelers out for possible masters for Aang. Attempted to find firebending academies similar to Master Yu's. Tried to learn at least the basics of firebending, regardless of its application on the Day of Black Sun.
Because to be a fully realized Avatar, he did have to know all four elements. Learning firebending was going to be the most difficult for lack of a teacher, and that was highlighted when the team first arrived at the Western Air Temple. But it could have been a pressure for the team starting with season 3.
Each village they visited and each story we got could have still happened, but it would have been better served if the team attempted to find a master for Aang, and always came up short. It would also lead to the same realization they have at the Western Air Temple, that they really have no choice but to accept Zuko's help.
And it would have fit into Sokka's strict scheduling, which includes trying to master firebending as soon as possible.