They key to singing great is efficiency. If our voices are not efficient we end up having all kinds of problems from "pushing the voice" to lack of power and range. We have to understand vocal registration and the vocal vectors.
Vocal registration includes things like falsetto and chest voice. And we must develop both fully. The Vocal Vectors are the up pull, down pull, back pull and forward pull of the larynx. Registration affects the vectors directly.
Since the Vocal Vectors have 4 different directional pulls it is important to balance those pulls properly. Too much pull from one vector throws the larynx out of proper position of the larynx when we sing. Depending on which vector is out of balance determines which result we get. For example, too much up pull can give us throat closure.
The technique is was taught is based on balancing the vocal vectors which absolutely involves developing the chest and falsetto registers. This balance is what every great singer has. No great singer was unable to sing in chest or falsetto. People wonder how great singers do what they do. And this is how; the balancing of the vectors.
Many people look back at all the great singers in history and do not understand that what made them great was that their voices were not blocked by constrictive tension. The idea of "singing with an open throat" is often thrown around in the singing world to describe what a great singers do. And you can read a million different articles on how to achieve it. Or have hundreds of voice teachers who tell you different ways to get it. The best way to understand it and to have a clear way of how to do it is through the balancing of the Vocal Vectors which includes proper vocal registration.