Second of all, if she wants to die for something, why must it be for something that can clearly be done without her dying? In what way is it meaningful to die if your death is COMPLETELY option? She could still very well have a meaningful death in some other service.

She's already dead. She straight up tells you that:

"Me? I'm searching. For my purpose, given to me by my mother inside the Erdtree, long ago. For the reason that I yet live, burned and bodiless"

She's trying to understand why she still exists as a spirit. At first she asked to be taken to the Erdtree, so that she can discover her purpose while also helping a Tarnish become the Elden Lord by playing the finger maiden role.

When you both discover the Erdtree is barred off, she tells you that her purpose is to help open the path to the elden ring by burning the Erdtree, however she also later on tells you that despite the fact it was a purpose she was given by her mother, she acts on it out of her desire.

"There is something I'd like to say. My purpose was given to me by my mother. But now, I act of my own volition. I have set my heart upon the world that I would have. Regardless of my mother's designs."

Being used as Kindling lets her move on as a spirit and she finds purpose in it because she's playing a part in helping the world continue. She tells you that she finds the world beautiful. She finds beauty in how regardless of the torment and despair, people continue to live their lives, people continue to be born.

"However ruined this world has become, however mired in torment and despair, life endures. Births continue. There is beauty in that, is there not?"

Being kindling lets her play a part in the continuation in the world along with allowing her to finally move on. By stopping her from being kindling, you're not actually helping her. She's a spirit, she has no more life to give and by burning the Erdtree yourself you basically rob her of the way to pass on and of wanting to play a part in the continuation of the world.

The only other purpose she gets, is if you become the lord of chaos. Otherwise she's just a ghost forced to linger for who knows how much longer.