I'm curious if maybe the mistake was in assuming we needed AI for the teaching part of the process.

Maybe we should focus only on having AI for the correcting/internalizing part instead? A purely deterministic grader and problem creator creates an endless stream of problems and solutions. The LLM's job is just to help you get to the point that you can assign a random problem from this problem set and the student will be able to answer it without assistance. Hopefully the teachers lecture at the beginning of class helped with understanding as well (I suspect that it would), and also provides a more broad "theory of mind" about what we are doing than the myopic LLM's "Let's get you solving this problem" does. Also, humans are social creatures, and being taught by another human being (even if it were less efficient) is likely beneficial to most people.

tldr; Normal human teacher, deterministic grading to gauge progress, and LLM assistants to help the student get to the point that they can pass the deterministic grading.