The problem is that the student is in charge of the tutor and often tells them to just do their homework for them and not check whether they have learned anything.
LLM providers should formalize a tutoring mode. We should have prompts available to create this mode. This should be the default way students use LLMs. LLMs may not be good enough to do this now, but I think there is already enough raw intelligence and its a matter of training models to be good tutors, to be experts and specific subjects, and developing software systems for tutoring.
In this model there are few lectures. This is more similar to Montessori but with on demand tutoring. The teacher provides objectives and materials for the students and tutors. The tutoring process can be done during class for teachers to ensure it is working well. There can be larger blocks of office hours for students to do their tutoring during.
As AI gets more intelligent, it will also be capable of doing all the grading. This includes oral exams. Teachers need to proctor the exams in person.
Anyone will be able to tutor themselves on any subject. Proctored examinations to certify knowledge do not need to be very expensive. The value of the school environment will not be to transfer knowledge from a teacher but to have peers working on the same thing and teachers and an environment invested in training the next generation.