As I learned from "voice building" expert Gary Catona, while breath management and phrasing are basic skills that will help any performer, this seems to be the only thing taught by the majority of vocal instructors, at the expense of more precise and relevant exercises that focus on muscular strengthening of the vocal apparatus itself– the larynx and pharynx! 
 

The often heard claim is that your primary focus in singing should be the diaphragm muscles which support the voice, which then "floats" on a stream of controlled air. But this is just plain incorrect.  Sound waves, created by friction and resistance of the vocal cords against air, are shaped inside the throat and mouth, and then travel through air! So yes, it's important to breathe well - but even more important to have control over your voice muscles!

click for a link to a quick illustrated explanation of how the voice works
Many teachers also favour a particular style of delivery and try to teach you to sound just like them, or give you a technique that is hard to apply to your style.  I often have heard singers say things like: "Should I study with a classical teacher? What if I'm doing rock or musical theatre?"

The main thing is to develop your instrument so it can do what you want it to do, so that you can sing with power and control, in ANY style! I focus on what you want to do with your voice, and can help you reach the performance level you're aiming for, even down to giving you focused direction when you're tracking.