Well, if that's what people need, then we shouldn't be wasting the time of tenured professors and grad students—who have much more interesting and specialized things to do—by making them into whip-crackers. I think the ideal "teacher" for a completionist education system would simply be someone who could juggle the roles of motivational speaker, hard-ass, and Socratic. In other words, although they would have their own particular skillset, they wouldn't need to know the material at all.

Lecturing would be left to professional speakers backed by a writing team and subject-matter experts, filmed remotely and either sold to schools as materials on the free market, or produced for the public by government media arms such as the BBC. If anyone had a question about the material that couldn't be answered by the lecture, the books, the rest of the class, by the "teacher"'s Socratic deduction, etc., the school would have tutors on-call as well (by remote from a tutoring group, or locally as a service of alumni.) There would be no segregated "classes" or "classrooms", but rather an integrated environment more akin to a combination library/study-hall, with gatherings for people working on the same class of problem at the same time, etc.

In fact, there wouldn't really be a need to "graduate" at all, or to "register" for specific semesters. As long as you could get a print-out at any time proving you had 100%-ed the problems relevant to the job you're applying for, that would be all you would need. You would be able to show up one day, leave for years, then come back and resume your studies as if you had never left. In fact, done this way, people would probably stop considering themselves to be "in school", but rather just say that they "go learning" in the same way one would "go hiking" or "go to yoga." A life-long hobby, in other words—just the way an education should be :)

Ah... but if only.