I look at it this way: if Aang just killed Ozai, it would've just been "meh" to me. Whether he killed him outright, or if Ozai did the whole "rawr your back is turned now I will attempt to stab you with this knife I conveniently hid in my pocket" letting Aang kill him guiltlessly. It's been done so many times before I was really expecting him to, but of course, in keeping with Aang's character, he learned to be decisive but to not compromise his ideals. Besides, this way Ozai gets to witness all that he and his tyrannical forefathers built up, fall with Zuko's more progressive and benevolent rule. Ozai and Azula's defeats are cruel,
cruel mercy. Also the creators said that Azula was sent to a mental asylum on an island in the Fire Nation. Possibly with a room full of mirrors so she can claw at hallucinations of her mother.
Also, watching the show while keeping in mind that each people are slight caricatures of the Zodiac makes it a bit more intriguing. Earth= stubborn, proud, immovable; Water= emotional, idealistic, caring, maternalistic; Air= independent, aloof and detached, intellectual, humanitarian; Fire= aggressive, dominating, passionate, very loyal.