system
Given the following post, respond as if you're commenting on Reddit:
human
[Avatar] Why do benders only live in their respective nations?

If I was a waterbender, I'd learn to heal, move to another nation, and then charge through the nose to save people's lives. But they're not doing that. They all stay in the water tribes where their skills are basically worthless. The same goes for earthbenders who seem like they could make a killing in the fire nation. And fire- and airbenders could probably do something cool with their powers too that will be worth more when they're rare. But this doesn't seem to have happened. There is maybe one airbender left in the world just because this didn't happen. Why?
gpt
For what we saw from Wan's backstory, the world of Avatar has been in conflict since Vaatu was released and the humans started roaming by themselves (maybe even before that, and that's how they ended up in the back of the turtle lions), first with the spirits, then with each other. 
The following era might be a series of war not between nations, but between tribes, with warlords regularly emerging to try to unify all the benders of one element or all those living on a territory. 

Smaller nations would start to form, and benders would start to seek for terrains that gave them terrain advantage over possible enemies. Firebenders took boats and traveled to an archipelago full of volcanoes. Waterbenders did the same but went north and south, with some staying on the swamp. Airbenders keept being nomads but build temples on the tallest mountains. Earthbenders remained in the continent, that had enough earth to protect themselves. Most non benders remained too, but those who were friends or family or were members of a small nation of mostly benders were took with their respective groups. 

Wars of unification and fights for the power were still happening, until the big four nations were formed and some kind of balance between them was obtained. As each nation remained to themselves, leaving their hometown was not well saw, so travelers were few, but i'm mostly sure there was at least a water tribe doctor on the fire nation at some point, it just didn't happen in the time we saw. 

Then the war broke up, and any fire bender that was living on the earth nation or outside the fire one was probably chased out or worse, even if they weren't fire nation loyalist. 

It is only after the end of the war and the creation of republic city that the people are motivated by the avatar to leave their home places and live among different people, and we start seeing marriage between benders of different nations like something is common. 
And again, i'm sure the daughter of Zuko has a water tribe doctor on her court.