There should be a title of Graduate Advisor, and Teaching Professor (those who teach others to become a professor/teach in a classroom). There should be specialization on being an effective teacher. There should be pathways to success. Pushing all students into research and half heartedly force them to learn how to teach only re-enforces this idea.
For those "graduate professors" who just consider advising and mentoring grad students teaching, you have to apply that same logic that by mentoring anyone in the field, you're now a teacher. (That's a dualism)
My big issue here: we're completely ignoring the issue that a student comes into the university to learn. (Even if it's a research institution) By assigning "professors" that don't actually teach you're doing a huge disservice to everyone. In those cases students are left to their own devices, they're not going to do well for research, community, or industry. Really what's happening is people are paying for an apprentiship to become a researcher.