In order to get somewhere with functional training, a teacher has to pull in two opposing directions and that is confusing to the student. It is very well stated in William Vennard’s book Singing: The Mechanism and the Technique. The teacher has to get the singer to be both flexible and strong, and the mechanism to be sturdy and malleable. The sound needs to be “bright” but also have some “warmth”. This is usually described as being “chiaroscuro”or clear and obscure at the same time.
If you work only in one direction, sooner or later you will dead-end. You need to get the voice to have a strong healthy chest register response but if you only work on chest register you will find that the voice gets stiff and starts to have various problems like flatting and constriction. If you work to develop and strengthen head register to make it stronger you will find the high notes flying out with little effort and the soft tones easier to do, but you might also get weak on the bottom and end up without warmth in the tone in the middle. Either way, you pay a price for not being balanced in both registers.
The work in the voice is always in the middle. It is in the middle that mechanics matter. If you do not know how to mechanically adjust in mid-range, you will never sing easily in a wide range of pitches. And, if all you can do is sing in mid-range, you will never have a strong bottom and easy top. Either way, you will be limited.
If you expect the middle range to take care of itself through random vocal exercises, you will waste a lot of time waiting for it to “arrive” in a finished state. It is only through deliberate cultivation of various vowel and register responses that the middle voice can come into its own and that takes both time and practice.
If you study with a teacher who asks you to do something to “get lighter” and then, a few weeks later, she asks you to sing with “more fullness”, that might sound contradictory, but it would mean that she is a good teacher, who is seeking to strike a balance between two seemingly opposite behaviors. Somehow or other, they can coexist, and in fact must coexist, if the singing is to be secure.
And, while working on the typical things like “breath support”, “resonance” and “placement” could be useful, they could also be useless, depending on how they are approached. The teacher has to have a good deal of knowledge about how to cultivate a balance of registers and vowel sound configurations in order for things to be coordinated with breathing.
Functional training is hard to do in many ways because it asks for a wide variety of abilities that take time to absorb. It can be confusing to a student to be told to “do this” and then “do that”, but in the long run, that’s the only way to go.