> You aren’t doing work given to you by the university or your advisor.
Something tells me you have not been through PhD, or are have not interacted with other PhD students. You absolutely work on what your PI got their grant for.
It's safe to say your experience is highly atypical. Even if a grad student's stipend is not funded on an RA for their research, the research still costs money. It is certainly funded from somewhere, and it's not coming from the tuition. It's almost always the PI's grant. And that means your research is on a specific problem.
I can't speak to what your experience is, but what I am saying here is typical in US universities.
Something tells me you have not been through PhD, or are have not interacted with other PhD students. You absolutely work on what your PI got their grant for.