Two questions; what would Mathilde gain from the position, and what would the position gain from Mathilde?
What we'd gain:
We'd be able to shape college policy.
We'd have direct access to the heads of the collages and be able to influence them.
We'd have direct access to the Emperor and his council and be able to influence him.
We'd be able to deploy wizards and battlewizards to pretty much anywhere in the Empire.
We'd be able to access the libraries and archives of the eight colleges.
What we'd bring:
We have unique insights in to various, hostile types of magic, and could pass those insights on.
We have close ties to the dwarves, and could bring in their knowledge and skill into aiding the collages (like we did with the training rooms).
We're close friends with both the Empress and the Elector Count of Stirland, and can influence the Empire through them.
We are building connections with both the Eonir and the Cult of Ulric.
We have connections with the Cult of Ranald.
Are we the best candidate right now? No. Do we have any ambitions that would directly benefit from the power and authority of the position right now? Also no.
But the position in question does hold much value, and we do have connections and skills that can benefit the Empire from such a position. Honestly, the whole thing is basically "Court Wizard to the Emperor", and that's not too different from "Court Wizard to Karak Eight Peaks", except that K8P doesn't need a court wizard anymore and the Emperor's current court wizard is doing a grand job.