I think it is interesting how important Nienna would end up being, that she was the teacher of Gandalf. Because a major underlying theme of Tolkien's writing is hope. And if Nienna is the Valar of grief, how do those fit together?
The thing is, I think Nienna is also the Vala of empathy. In order to truly grief for the pain and suffering in the world, when you are a Valar who does not really feel that, except maybe when you take a body that you can then easily discard, empathy is necessary.
The other Valar often seem very removed from the world. It isn't that they don't care, because they do. But they still seem distant, separated. Nienne, in her grief, sees the world. She feels for the suffering of all the beings of Arda. She cries at deaths. And she teaches Gandalf to feel that grief too and to feel that empathy.
And I would also note that in grieving for the world as it is, for the suffering of all people, she is also grieving for the world that could be and yet is not. And that is hopeful. She has a vision for how the world should be, she sees how it is broken, and she grieves.
And of the five of the Maia sent to Middle Earth, it is Gandalf who becomes most invested in the world and its inhabitants. It is Gandalf who feels empathy, who sees the peoples of Middle Earth. And it is Gandalf who is ultimately the one who is able to remain fully faithful and succeed in the task that they were sent to achieve.
And empathy is possibly the most important thing in the ultimate destruction of the Ring. The empathy towards Gollum by Bilbo, Gandalf, Frodo, and Sam is what allows Gollum to survive and ultimately leads to the Ring'd destruction.
So I personally think that in being the Vala of grief, Nienna is necessarily also the Vala of empathy. And that is what ultimately saves Middle Earth.
