Teaching voice is a complicated thing. Not only is the instrument extremely personal to the artist, but it also takes considerable time to isolate individual parts of your vocal anatomy. Continuing on past that how you use your vocal instrument changes depending on what genres you are attempting to sing. For instance, current pop music is leaning heavily on a breathy or stiff vocal production, while musical theatre is in a heavier or thicker production and loves its belting.
With the differences between different styles, it is important for students to explore multiple genres of music during their lessons. Singing and experiencing different vocal productions opens up more choices for each performance for the student.
It is a common opinion in the classical vocal world that the best vocal style is that of opera or art song. The accuracy of that statement is really up to the listener. I would agree if you are singing opera an operatic technique is the best but we all have also heard an opera singer sing anything else, and it wasn’t good, and by that I mean it was technically correct it just sounds wrong. A well-rounded singer can produce whatever sound they want to.
There are several other considerations in voice lessons to consider. Traditionally voice lessons are taught without amplification, however, all of the commercial music is performed with microphones. While it is certainly not necessary to do every lesson with a microphone it is important to learn how to work with a microphone, monitors, less than perfect distance from your band or accompanist.
It is my opinion that students should learn and practice songs from a minimum of rock, musical theatre, and classical music. The rock and classical music will in many ways develop opposite skills most notably in classical you will have a tilted thyroid cartilage producing vibrato, while vibrato is not widely used in rock music, this control is important for the success of musical theatre where vibrato is used only at certain moments. You will also end up using different configurations of the true vocal folds to produce different vocal qualities across the three genres.
Like with all instruments, the goal of learning to sing is to sing as well as you can and to have fun. The more control over your instrument, the more music you will feel that you are able to successfully perform. This will increase the enjoyment you have when you are singing.