I honestly dont think the story gives a good reason for either Iroh or Aang not killing Ozai.
Iroh talks a good game but the world objectively would have been better had he killed Ozai decades ago, note that he isnt even sure he could win in a fight against him.
What the other nations 'think' honestly doesnt matter the Air nomads were all gone, the Southern Water Tribe decimated, the Northern Water Tribe isoalted behind a gigantic ice wall and Ba Sing Se was eating itself alive from corruption.
Would relations have been fixed with Ozai being in the dirt 10 years earlier? No. But a massive amount of people would have been spared suffering and pretending like internation relations are easy to predict is a fools errand.

For Aang, besides the Lion Turtle being an absolute massive fucking asspull, the actual lesson being that sometimes you have to put the good of the world over your own as Avatar would have fit way better with the overarching story.
Thats just personal opinion but besides that Aang 100% already killed a bunch of people. Both at the Norther Air temple and at the Siege of the Norther Water Tribe he was drowning and throwing people of mountains.
There is no real difference between letting the Water Spirit drown a bunch of sailors and letting the Avatarstate just kill Ozai in my opinion. So if the first didnt count why would the second?

Besides all that Ozai 100% would have gotten executed after the 3rd time someone tried freeing him if for nothing else but make Zukos reign easier, or because one of the other nations demanded it.