There are strict non-interference laws in place that prevent the Spirits from directly influencing the physical realm. This is unless:

1) The physical realm encroached on them first (this is in the case of Koizilla and Wan Shi Tong) or

2) They willingly submit to joining the Weave of Destiny and offer themselves to be part of the cycle - permanently.

To date, only one spirit has joined the Weave willingly - and as the World Spirit, this meant they knew that it wasn't quite a full submission to the Weave. Someone had to act as the Bridge.

- Other Spirits that join the Weave wouldn't be bridges.

So by this point the Blue Spirit was already nearly forgotten. Dragons were nearly extinct - there was no need for a Herald. The Water Tribes had completely forgotten that a Fire Spirit was once part of the Water Court. And the Blue Spirit mask was now just one of the theatre masks that got rotated through.

Sozin and his heir, Azulon, had stamped out systematically the old legends of the Painted Lady, leaving only one town that clung faithfully to their patron river spirit. The Painted Lady went from the Soother of Gajamina and one of the Fire Court's patrons of healing to being a local folk tale.

This of course essentially meant that they were 'retired' Spirits with no formal duties any more. Other Spirits frankly looked forward to this time as they could finally relax and cease all contact with the Physical realm.

But the Blue Spirit and the Painted Lady were no ordinary spirits - even if they were minor Spirits within their courts.

They had to do something, something to mend the Weave which was on the brink of ripping itself apart. The members of the Court of Balance were desperately trying to figure out a way to retrieve the World Spirit so that the eventual spill-over of war into the Spirit realm could be mitigated.

- The War reaching the Spirit Realm could very well spell the destruction of life all round as they knew it.

Once again, the Great Spirits kinda were just sitting around debating instead of doing anything to fix the War. And so two spirits slipped away determined to do their parts to mend things.

- The Painted Lady before she joined the Weave left behind an echo of her power to protect her last sect of believers.

Zuko and Katara don't know who they are but Zuko had an incessant need to look after his people. He from young knew that the War was making his people suffer. His attempts at fixing things culminated in half his face getting burnt off.

Katara's need to mend things manifested in making sure Aang fulfilled his part to play in restoring balance.