As I’m sure you know, Most PhD students stop taking classes by the end of the 2nd year, and focus entirely on research and teaching thereafter, which means that the “free tuition part” is just a sham to avoid classifying PhD students as workers, and to hence avoid paying them for their labour.

As a grad student you are there for an education and your education doesn't only (or even mostly) happen in the classroom. If grad students want to be treated more like employees and less like students, the relationship between student/advisor will shift more toward an employee/employer relationship. This may result in more pay but it will also result in different expectations. For example, if you want to be treated more as an employee, then I would have a lower tolerance for mistakes a student would make. If you want to be an employee I will start hiring for skills rather than potential. As employer/employee relationships have developed maxims like "fire fast", this attitude change may work against grad students.

Also just to be precise, tuition isn't just to pay for classes, it goes to pay for all of the resources you use as part of the university community. If you are done your requirements you will still have to pay tuition. And students don't stop taking classes by the end of year 2 (or 4 depending), they stop taking required classes. Since your advisor pays your tuition, you can negotiate with them if you want to take more than the minimum. You are done your requirements after 2-4 years and don't have to take more classes, but of course you can (I did). Maybe this is something unions can help with.

This.

My indulgence for "I spent three months going down this rabbit hole because it might have proved interesting" is way hired for graduate students than it would be for research staff, because that's part of them being students.

Not to mention that PhD students would mostly be self-learning anyway.