Honestly I thought it was appropriate. Aang, a freaking teenager, has an entire mini arc about the moral canundrum of having to kill someone while the fate of the entire world rests upon his shoulders. They also established how strongly it was against his religion to kill anything, and that he's a vegetarian.

Obviously it was a copout in that they can't show a character being directly killed in a spectacular enough fashion for a series finale on a children's show, but ultimately weakening the big bad evil guy and taking away all of his power, politically, physically and emotionally. That's a great place to end it and so very in character for Aang