And this is a little retroactive since the ATLA novels came later, but Yangchen DID have regrets. She tried to Be The Avatar the Right™ way and it just didn't work. Then she started politicking, spying, manipulating, blackmailing, etc., and that actually worked really well! ...but sometimes too well, because she also sometimes got people hurt or killed.
Killing Ozai is a very big ethical and moral quandry for Aang, and every Avatar he spoke to tackled a different thread of that giant knot. The one Yangchen tugged at was the question of what point the ends stopped justifying the means...and what one can or should do until that point.
Also, I haven't seen the finale in a while so I may be wrong, but iirc none of the previous Avatars technically told Aang to kill Ozai? They did all talk about things like decisiveness, permanence, embracing violence when necessary, etc. -- which, in the context of what Aang was asking them in the first place, certainly come off as sounding like condoning killing Ozai. But unless I'm really misremembering the finale (again, entirely possible), none of them actually, explicitly, and specifically said Aang HAD to kill Ozai, or that Aang only solution was Ozai's death. All of them, in different ways, turned out to be right.
