Everyone has a point about this. The comment about this in golf is right on the mark. I saw David Leadbetter, the golf pro, on a TV. He works with a lot of people at his school in Florida, then later will give advice based on emailed video clips. So, I guess he does this, but only after he's worked with them in person. Someone in my family went to his school and Leadbetter could tell almost everything from observing one practice swing. Although he's quick to admit in some interviews that I've read that he's never 100% sure that what he says is the right thing. So, he's big enough to admit that he makes mistakes. That's a big part of effective teaching.
I think part of the problem with doing this with skiing is that you need both frontal and side (and possibly rear) videos to have a really clear idea of what is going on. I think it's also tough to give feedback this way because good instruction always demands a real time discussion between the intructor and the student. Tough to do that with email and video.
I think you've also got to take instructor input with a grain of salt. I skied a few weeks a go with a guy I used to race with. After a couple of runs, for no reason, he said, "You've got to use the front of your skis more." Now, I ski pretty well and am centered. The skis do the turning and the whole edge engages when I turn. I can also vary the turn type and shape. In short, as another racing friend said, "He was just boosting his own ego." I think that that may be why a lot of folks take instrucotrs to task on this site. People just building their ego are really counter-productive. Good teachers just don't do that. From what I undestand, Leadbetter doesn't do this in his teaching, which is why he is so popular and effective.