I feel the basic marketing principle behind expecting an entire student body to be interested in the happenings throughout the entire university is flawed - the math majors aren't interested in who the visiting poet to the English department is this week (if this is the type of information that is shared). If they are modelling what engagement should look like off the percentage of fans who like / share a post compared to something like the university athletics page, they are going to be disappointed.
The faculties sharing the generic status with everyone's weekly happenings seems similar to having an important page two clicks from the home page instead of one: why would I want to search through 20 faculties' updates to see what's on in the psych department when, as a fan of the psych department, the psych department could have posted their schedule themselves? I understand the idea behind having all the departments contribute, but it seems to misunderstand the audience and how they want to consume information. Facebook posts rely on the browsing attention span of the audience, which isn't long!
Facebook's algorithm will rank poorly-shared content in quite a low location on the newsfeed if people have their newsfeeds sorted by Top Stories, which is the default. It's hard to say exactly how their algos work (although a lot of study has gone into this in a similar way to how people have studied Google), but a page with 195k fans whose posts routinely receive 20 likes will not be assigned great metrics on the back of that.
My alma mater has fairly decent engagement (40k likes; a couple to a few hundred likes on popular posts, but as low as 15 on less popular stuff). Every post gets just a few shares and a little more comments, but keep in mind that a comment or a like will make a public post show up on that person's timeline as well, so it's similar to a share in terms of visibility (I am not 100% sure about how the placement of a post changes on others' newsfeeds depending on whether their friend has liked, commented or shared, however). What my alma mater is doing, however, is posting university-generic stuff, not news about specific departments unless it's catchy or particularly interesting (the PhD. in squirrel psychology did well because it's a) cute and b) odd; interestingly they did not link to the relevant faculty and I can't find a press release or course page, which seems like a big oversight, even for new news!).
I would contend that a federal model (if you like) of marketing with a bit more power given to the faculties would work - things of interest to the faculties are dealt with on their pages whilst the central university page deals with generic interest.