This sounds like a very strange system to me. Where I graduated (and I believe in most of Europe) the university has to have allocated the full funding for the entire PhD for a student before that student is admitted. So the university cannot afford to run a scheme like you describe, which is good since that sounds to me like a borderline predatory system.
Teaching positions for grad students aren't predatory. They are really a form of financial assistance. In return for teaching 3 hours a week 2 hours sitting in your office with the occasional student visitor (with say 5 hours of prep work that could be done during office hours and 3 12 hour days grading exams). That's 8 hours of work a week which works out to a pretty decent hourly salary.
It's hardly luxury and when the state/university system yanks funding out during your tenure THAT is somewhat predatory but usually most departments find a way to tighten belts and make sure current students have sufficent funding.
I've got six hours of teaching a week plus 2 hours of office hours plus meetings related to teaching plus prep plus grading.
Plus classes, homework, exams, plus research meetings, plus doing research, plus seminars, plus commute.
My university's administration has a rule that our department can't pay us more than a fixed amount, and that amount happens to be lower than the living wage in the city I live in. In other words, by the university's own admission they don't pay us enough to live off of.
