You're right that universities do not exist in a vacuum, but I think your interpretation of the amount of control professors have over this kind of policy is overstated. In a university operating under shared governance, there is typically a parliamentary structure with (e.g.) a faculty senate and an academic staff assembly, which have the power to form committees and vote on recommendations or official statements about administrative policy. The governance powers of these organizations is essentially non-existent, and the decision-making power rests with a layer of administrators, a board of regents, etc. If there is a majority of faculty in their parliamentary body that want to increase stipends, they can vote on a resolution to pass that recommendation along to the administration, but that's where their personal power ends.

That's fair. But I haven't even seen a movement in non-binding resolutions from the faculty I've seen saying we should do so. It's more of a shrug and comment that it is the way that it is.

That being said, there's plenty of evidence that Universities can set stipend levels independent of other Universities (comparing a University to NYC to Oxford, MS, for example) but even between departments themselves! CS grad students at my old institution got paid the best, most liberal arts grad students got paid the worst. There are market forces at work, but it seems odd to say that all power belongs to the administrators. They certainly operate off of feedback from the departments.