It is necessary to have a system of teaching that is both clear and fluid. (Chiarofluido?)
Rigid systems or methods have a set way of teaching and individuals are not allowed to vary from the set principles in any way. There is “one right way” and that way is the “best”. Things have to fall in line with the system or they are “wrong.”
The other way is that everything is chaotic. Each moment, things are made up, randomly, without any regard to what was previously done or what will follow. There is no order, no form and no consistency, in the name of “freedom” and “spontaneity”. Setting things into a framework would be discouraged or even frowned upon.
Such systems do not work. Sooner or later they break down or the people adhering to them end up locked in a box or just plain lost.
Sadly, there are plenty of people teaching singing who think one of these approaches is best.
Not everyone is there, thankfully, and that has always been so. Most people pick and choose what works for a student but with some sense of order or a goal of some kind in the back of their mind. This is the safest way to work, and the most practical, since we are all so different.
It is, however, a very slow way to work, as it takes a very long time to recognize patterns, tendencies and issues that come up over and over in a variety of singers who fall into several general categories. Addressing these things repetitively, over a length of time, one begins to recognize that there are certain kinds of behaviors that are typical of (a) untrained singers, (b) singers who “over do” and (c) singers who don’t “do much”, as well as those who have a history of pathology and those who have other issues like poor intonation, lack of coordination and musical illiteracy. Usually, a teacher is doing his or her best, but it takes a long time to recognize your own foibles, too, and the kinds of things you don’t notice, forget, or are just not very good at yourself (which we all unconsciously avoid).
A good system has flexible boundaries but clear guidelines. It has a structure but that structure is adjustable. It prevents the teacher from getting lost and the student from floundering. It allows the teacher to communicate well with others about their students but doesn’t make for all teachers being the same in a “cookie cutter” way. It sets up patterns and explains tendencies and gives remedies for attending to them but not without a degree of creativity to find new solutions to old problems all the time.
If you don’t want to waste years figuring things out on your own, alone, go study a system of teaching singing. Doesn’t have to be mine, as there are plenty out there, but measure the criteria on what I have suggested above.