When I hear about the invitation from someone to sing naturally, in an inspired way, as a solution to a technical issue, I hardly agree.
Many do already sing well-connected to their artistic side, with emotion and a natural talent in "feeling".... their problems often are not related to Art, but must be ascribed to Technique.
These singers come to us with a problem and they want a solution. It's often an incorrect use of their body to prevent the blossoming of the singer's voice, and the invitation to "be natural", to "feel", to try and express more in most cases yields no significant result.
Of course, in order to have a "complete" singer, you also need this connection... but a good teacher must be able to identify and remove any existing mechanical impediment, then he and the student will instill a more efficient coordination which responds to the laws of physiology, acoustics and phonetics under which we all operate. Then everything falls into place.
On the other hand the attempt to awaken sensitiveness in the subject that for too long has left this skill dormant calls for a much longer and often unsuccessful process.
If it is emotion that lacks, and if the singing feels devoid of that magic, of the inner dimension and, ultimately, of interpretation... well, it will be quite difficult to bring back artistic sensibility (the ability to experience, to recognize, appreciate, and to reproduce emotions) without educating in a very broad sense the culture and life experience of the student.
It must be remembered that often these skills are already present in the "natural singer"(and that is why he or she wishes to have a freedom in the use of their voice: they want their instrument to be able to go hand in hand with what suggested by this inner world within!).
In my experience, the hindrance is often of technical nature(read: mechanical) and I'm sorry to say that the teacher who cannot link the effect to the cause and doesn't know how to precisely cure it, for as mystical, inspired and inspiring as this teacher can be, simply is not qualified to teach singing.
If I had to sum it up, almost often it is because Technique is wrong that Artistry has no way to come to life. On the contrary, all the feeling and sensitivity of the world are useless if a problem caused by improper coordination be not addressed and the correct physiological process be adequately restored.