There is no such thing as good generic training for anything. General study produces general results.
One of the basic tenets of acting is that all choices have to be specific and clear. You can’t be “kind of angry” effectively when that’s based on some kind of mood. You can’t be doing anything that requires focus if you have none and that includes things like skiing, cutting up a log with a chainsaw and cooking a delicate soufflé. You have to learn to direct your attention, concentration and mental clarity to the task at hand and stay there until the task is completed. Distraction of any kind is not good.
Students, however, are frequently criticized for “thinking too much”. I always find this a laughable instruction. “You are stuck in your mind”, they are told. “You are watching yourself sing.” Perhaps so, but why is this bad?
When was the last time you were instructed to do something new and complicated in front of someone else and executed that task with no thought whatsoever? The learning process begins slowly and often self-consciously and “thinking about it” is necessary for a long time. In fact, if you do not think about it, it never happens. If, on the other hand, you have been asked to do something that is beyond your capacity no matter what you think of (happens all the time) or you have been asked to do several new and difficult things at once (ditto) you will be left with a mess and remain self-consciously confused and stuck regardless of thinking. If you are then blamed (again ditto) by the person who gave you the instruction by being told, “You are thinking too much”, you are left to feel stupid and inept.
In order to learn to sing rock music you have to prepare your throat to make the sounds that are typical of rock music. If you do not listen to rock music, you won’t know what those sounds are. If you do not make them yourself, you will not know how they feel. If you do not know how they are produced by the vocal mechanism, you will not be able to teach them effectively or learn to do them easily without help. You can’t teach what you do not do and you can’t do what you do not understand. That flies in the face of common sense. But, in singing, people do it (or try to) every day.
If you want to learn to sing jazz, or country, or any other style, including classical, you need to know how mainstream successful artists sound when they sing in those styles and you need to know how to replicate those sounds yourself or help others do so if you are teaching. Since there are still, at this time, very few CCM teachers who have anything other than classical training, and very few CCM artists who understand vocal function, that means the probability for generic teaching is very high. Thinking that “classical training” (whatever that is) will help you sing everything because “one size fits all” also flies in the face of common sense, but that doesn’t stop people from having those beliefs or acting upon them.
Specific training is necessary for specific styles. If you want to learn to sing in one of them, find someone who understands how they work and how to communicate effectively to you, personally, exactly what that entails in terms of skill building.