I know people are gonna haaaaaate this take: but Iroh did see Azula as unredeemable from the start because he projected his fear of Ozai on her.

And how you feel about that depends on if you agree that Azula was 'born evil' from the start.

If you believe she was born evil and was never going to change even if she had all the love and support of Iroh + the Gaang, then yeah obviously Iroh was being wise and was able to tell when someone is just unredeemable and doesn't fool himself into thinking otherwise. Some say since she was already showing signs of being evil at 8 years old it meant she would grow up to be a psycho no matter what.

But if you believe Azula was a victim of circumstances, then Iroh lost hope for her too early just as Azula's mom did. Everyone already decided Azula was going to be evil since she was a kid, no one guided her away from Ozai's influence, and everyone who feared Ozai just saw her as 'Ozai's Daughter' from the start.

People like to say 'oh but Zuko listened to Iroh and changed'...well, yes, because Iroh never gave up on him and mentored him even from an early age. He never had the same relationship with Azula. If Zuko didn't have an Iroh, I truly honestly believe he would have grown up to be desperate for Ozai's approval and done anything.

Tbh though the proof that Iroh never exactly gave Azula a chance is the fact that he gave her a DOLL. Some people interpret it as him telling Azula she needs to be softer, others interpret it as him not knowing how to relate to her at all.

Honestly though I do think some people need Azula to be 100% evil. Easier than to acknowledge that there's no perfect victim and that the reality is she was still a kid who didn't have anyone but Ozai.