While not a new idea to me, I have recently become conscious of the prevalence of lessons-via-media, specifically the Skype lesson. It seems that they are not just an "option" as they once were. They have apparently become positively mainstream.
Personally, I am wary of this phenomenon. Perhaps more than wary. In fact I admit to having an actual problem with it. I simply don't think that any teacher should take their standard fee based on any non-live experience of a person's singing. Anything piped through technology is suspect. Not suspect, of course, of any sort of auto-tuning, or the like. But even the simple fact of it having to be transmitted electronically.... It simply isn't the same thing, and I think there is something teetering on unethical about a teacher saying that they can promise to give their full, accurate aural attention and diagnostic capacity to something that is secondary (transmission) or tertiary (transmission & amplification equipment) to the live event itself. I personally do not do it because I feel I can't guarantee the best of what I can offer in the moment.
I did once offer, at a significantly reduced rate (more for my time than anything else) to do some remote work with an already long-time student on a very short-term basis, and was somewhat relieved when this need did not materialize, as I felt uncomfortable with it from the moment I agreed to it.
As an audiophile myself, I will be the first person to say that we have amazing recording capacity, and that the technology is impressive. It has brought hours upon hours of listening enjoyment to people. But any person who has listened to their favorite singer on recording at length and then heard them live will tell you.... It just isn't the same. And it is precisely this difference that should make teachers of voice balk before they agree to an arrangement of this sort, when a young singer is trusting their voice to, and giving their money over, into a teacher's hands.