So this is all anecdotal, so take this with a grain of salt, but I wanted to chime in on the discussion about collaboration.
I studied physics as an undergrad, and I spent sometime in a lab studying Solid State Physics (which is essentially the Physics of Material Science). As a physics student, I had very little practical chemistry experience at all (like 2 semesters of freshman chemistry), so the first 3 months of my time there was mostly spent just learning chemistry. For some reason, my department didn't collaborate at all with the chemistry department, and I remember being super frustrated spending so much time learning chemistry basics instead of doing physics. And I know for a fact that there have been times where both the Chemistry and Physics departments were tackling similar or literally the same problems, often competing for a solution rather than helping each other.
From my perspective, I should have been paired with a Chem Major, and we could have collaborated to get to work much sooner, with me covering the math heavy bits, and him the practical chemistry aspects I was lost on. What instead happened most of the time, is the chemistry department would find a solution that worked, but they had no idea why, then the physics department would rejigger their attempt at finding a solution to understanding what the hell happened with the existing solution. The whole situation frustrated me to no end, and I wound up moving on.
My whole point here is that I'm sure that there are a lot of both problems that could use a fresh perspective from people of different disciplines and people sick of thumping their head against a problem that their skillset doesn't fit perfectly. Even in a modern context, where we have well developed methodologies and systems of communication, cooperation between departments at the same college can break down, and cooperation can become competition, or worse, at loggerheads with one another. In WHF context, cooperation is not at all easy or common between humans at different colleges in the same Empire, much less different polities or species.
Baking collaboration into the charter is probably the only way we'd see real progress in this regard, aside from one-off efforts spearheaded by Mathilde herself.
Ironically, when the plan first came out, one of the first questions I asked picklepickkl about was if the lack of enumerated focus would hurt the institution, so I do get those arguments. Despite that, I still favor the idea of collaboration being addressed directly because I don't think having Mathilde push collaboration without it as a founding principle will have any lasting impact aside from the individual projects she gets involved in. And that's perhaps more important to me than a small set of things we can't research, or can research but with a small malus because they aren't 'cooperative enough' at our Branch College.