Anyone who has ever taught in a classroom, given a shiur, or coached a sport is well aware that diversions are sometimes necessary for health of the class, group, or team. I used the word "diversion" only because that is the way the question was posed. I see no reason to micromanage competent, hardworking, or prepared teachers, instructors, or coaches. If their gut feeling tells them that a *regrouping* is needed, I think that their should be a respect for their instinct. On top of that, when a class needs regrouped, it generally needs regrouping in the present, not later that afternoon during math class, and certainly not on the cheshbon of another staff member.
I'm not sure that Rabbonim who share the opinion of the speaker (and by what I've witnessed, I'm afraid this opinion is not uncommon) understand just what impinging does to the morale of limudei chol staff and to the behavior of the students in class and towards staff. I have no major objection to spending more time on limudei kodesh than limudei chol, so long as a standard quality is maintained vis a vis general studies. If a school decides to dedicate 70% of the day to kodesh studies and 30% to chol, that is the prerogative of the school.
I do have an issue with the casual treatment of limudei chol in general. Such casual treatment is what leads kodesh teachers to impede on the time of fellow staff, infringe on the authority of other staff, and it ultimately leads to a lessening of respect, job dissatisfaction, and high turnover, all of which lessen the quality of the school as a whole as well as cause greater expenditure.
As far as I am concerned, every adult worthy of employment, deserves to be given a certain level of deference and authority. Their opinion should be valued as they are in the front lines. Their discipline should be supported. Their subject should be respected. Their time should be respected. They should have the authority to enforce their own (perhaps approved) classroom policies. In other words, their classroom should be as sacrosanct as the next.
I know it is very popular today to "teach middot" and I do know that many limudei kodesh staff are quite appalled by the level of behavior and chutzpah in many classrooms. I think the best place to start teaching middot is to review school policies and the environment and make sure that they are not undermining the lessons being imparted. As it has been said, "actions speak louder than words."