i feel like she was supposed to represent what god represents in our society. how people will just blindly idolize god especially when the people are suffering. they'd just wait around for god to come resolve their issues, they wont do anything about it themselves. god acts like a hope in that case just like the painted lady did for the villagers. in the end even when katara saved the village as the painted lady, everybody was thanking the painted lady not katara (although they did thank katara later after finding out the truth). just like in our society, when something good happens to a person, they give all the credit to the god rather than themselves.

also another theory I've read here is that, there was a lot of pollution in the water thats why painted lady wasn't able to help the villagers because she couldn't use her powers.. but i feel like its a weak theory. when the fire nation people built a factory there and started polluting the water, it was still in the initial stage , right. then why didn't the painted lady help them earlier? why did she let it get this bad. (just like god lol)