The thing about Spirits who've entered the weave properly is that once they've entered there's no way back to how they were before. When they are needed, they are brought back into the physical realm.
This means, much like the World Spirit with the Avatars, the Blue Spirit and the Painted Lady have become permanently intertwined with Katara and Zuko.
This also means that much like the Avatar, Katara and Zuko have memories of their past lives. But they are of course, not the only Katara and Zuko's to cycle through the Weave.
Unlike the Avatar Spirit who essentially are new people every cycle, Katara and Zuko are constants. Which means... far, far, far down the line. In an age of smart phones and wi-fi - rather much like this one actually, Katara and Zuko's spirits. The spirits of the Blue Spirit and the Painted Lady are... reborn.
