Ok, ignoring for moment what the thread wants Mathilde to do because the thread wants to see it, why does Mathilde want to do things?
What is Mathilde's motivation? What is she trying to prove, or accomplish, or obtain?
In the aftermath of the waystone and AV success, who is she as a character, to you?
Mathilde is an optimist, in the sense that she fundamentally believes in the power of people to make things go well. In this respect, she is showing her cards as someone from the Warhammer setting.
What I mean by that: Warhammer is, fundamentally, heroic fantasy. It centers individuals rather than systems or abstractions as the driving forces of history and the levers of the world. As such, Warhammer is extremely
agentic in its internal logic: it takes as read the idea that a person can make a difference, even in extremely entrenched systems. As mundane history, the concept that the Empire came back together under Magnus the Pious is
insane. It had been fragmented and at war with itself for a
thousand years. But between forces that can be explained by the setting's internal logic ("all the major gods publicly endorsed him as being a cool dude") and forces that can't (he was, in fact, just the coolest dude that there has ever been), the empire
super long divided did in fact unite, and not in a way where anyone is super worried about it flying apart at the seams any time soon either, which is wild.
Mathilde's life has been pretty shaped by this. She was saved from the pyre by the nameless watchman from her hometown; she discovered soon afterwards that the reason the law protected her at all was because of Magnus the Pious and Teclis. Her Stirland posting was a constant education in how the decisions of the people with power reshaped the world, for good or for ill. She toppled the Drakenhofs to finish what her lord had started, and even after his death Abelhelm's individual choices had massive impact on the fate of the entire Empire through the little list he gave to Mathilde. And then, of course, there was everything about Karak Eight Peaks.
So: why
shouldn't she believe that she can change the world? She's already done it multiple times. If she sees something she doesn't like, whether that's a dying Karaz Ankor or an Elector Count under terrible threat or a research project conventionally held to be impossible, she can put her mind to it and change it. If she sees something she likes and wants more of in the world, such as books, Ranald's strength and good repute, sketchy but not technically illegal magic, books, ways to perceive magic, books, or books, she can make that happen. And that's why I say she's an optimist: she can look at the world and feel hope, not because she's naive, but because she's experienced at changing the world for the better by her values and sees no reason why this state of affairs oughtn't continue. There isn't a shred of learned helplessness in her; if her noble motto weren't the thing it actually is, it could just as easily be the "It's Happening" meme.
Why does Mathilde do things? Because doing things
works.