Because it's a children's show than needed a happy ending, not some GoT level story development. A couple of comics highlighted some of these issues, though.
Realistically speaking, there would be a large portion of common citizens brainwashed by FN propaganda, blaming Zuko and how he ended the war.
Then we have numerous military officers and soldiers, war factories owners, bureaucrats and politicians that lost a lot as well.
Economical, political and military damage FN sustained was quite large.
All political&war prisoners were probably freed, and not every of those guys could just forget everything and live a peaceful life afterwards. How many Jet's and Hana's terrorists would be amongst them?
Finally, I believe Zuko didn't judged any of FN commanders for their crimes. This means, the ones that kidnapped and tortured other nation's citizens for many years are still free or even continue serving by his side. Water/Earth people won't be very happy to know about this fact as well.
So, to really bring any sort of peace to the world, Ava team needs at least a decade of hard work, probably much longer.