In regards to this (the other aspect):
In short, what I am saying is that doing something by the book (even if ONLY because it says so, rather than out of special insight as to why) can often be more useful than omitting that same act.
Tbh, I had never considered this either way. I was going from the premise that to teach something we ought to know about the subject and how to teach. I did not concern myself about whether one should do something by the book.
Ok, we have the scenario of inexperience. Supposing someone decides to teach music and is still a student, and has no pedagogy - something that happens often enough on PS. There are method books that were put together by people who thought things through, so that basic concepts are introduced in a particular order, music is organized in a logical way. Even if the teacher doesn't understand much yet, there will be logic in lessons when using such a series, and that will help both student and teacher. Otoh, an experienced teacher may see a reason for teaching this student differently, choosing different material, presenting concepts in a different order and in a different manner.
When we start out teaching we need guidelines. If we are thrown into teaching something we have not yet mastered then we want to grab whatever we can. That's the plus side of it.
But I have also seen harm which I have had to undo as a teacher because of blind following by my predecessors, and I have been harmed as a music student. I've taught generally bright students who were in major confusion because of how they had been taught, where the answer had been more of the same. I have seen causes for confusion in how we were told to teach, and I simply will not do that to a student. As a music student at this present time various harmful things are being undone with the help of a teacher who does have the capacity to think for himself and has thorough understanding, because of someone going by the (wrong) book without really understanding what they were doing, because the book said so, and the book was sacrosanct. Fortunately this was for a relatively brief period, but still long enough that it set me back by several years. And it was unnecessary.
On a personal level, if given the choice between a teacher who follows rules blindly, and a teacher who knows her subject, observes her student, and is a thinker, I would avoid the first and go for the second - simply because of my experiences both as teacher and as student.
AGAIN: my position is that formulas and devices are good TOOLS to use, as needed.