Why don't Universities pay PhD students more?
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.