Why don't Universities pay PhD students more? I've worked in higher education on the administrative side. I've been able to get a very thorough look at University budgets. From my perspective it's really a travesty that research Universities, with their multi-billion dollar operating budgets seem more inclined to hire largely purposeless administrators than to increase PhD stipends/wages such that a PhD wouldn't be so financially painful for students.

From my own perspective working in administration, it seems to me that the blame can be placed squarely at the feet of the near universal tendency for bureaucracies to naturally increase in size over time if left to their own devices. The discussion of why this is the case is beside the point, but this near universal law seems to be at work here. This limits graduate student stipend size because when faced with the choice of expanding the bureaucracy or paying graduate students more, the administrator - as a bureaucrat - will almost invariably decide to expand the bureaucracy.

That said, there are other dynamics at play in Universities that make me wonder why bureaucracies have been so successful at vacuuming up funds. Elite Universities often compete for top PhD candidates, so why haven't the competitive forces that drive up wages in the face of labor demand also driven up the stipends offered to accepted candidates? Are Universities coordinating to keep stipends artificially low? Or is the bureaucratic tendency to expand overpowering the market dynamics that would otherwise compel Universities to offer higher stipend packages? Or are existing stipend packages already at what we would expect the market level to be?
For students funded via the NIH and similar mechanisms (CDC and AHRQ come to mind), there are standard rates for what graduate students are paid. This is a fairly extensive treatment on the subject for one university: https://controller.ucsf.edu/file/4361

There are some ways to supplement this, but "This is what my grant pays for" is a very strong pressure on budgets, and departments often set grad student pay by policy in light of this, to prevent there being clear gradients of funding between students in their department.

Note that going over this by a lot via something like unionization can have extremely unintended consequences, like PIs suddenly becoming much more interested in postdocs.