I teach online via Skype, it's singing however, and it is certainly not for everyone. It works well for more advanced students, it's (imho) not so great for complete beginners though, and I would advise them to rather find a teacher close-by. Having said that: Good Skype tuition is a million times better than bad face-to-face tuition.
It becomes more and more common in the singing world. I get my own supervision with a world class coach, and I certainly prefer that a few times a year to one of the local teachers (I know the results they produce, and thanks, but no thanks). I am obviously a professional singer though who just needs occasional check-ups and can work independently in-between.
I agree that it is probably more tricky on certain instruments/possibly wouldn't work for all. There are teachers around though who insist on a "no touch policy" (I am NOT one of them, just playing the devil's advocate). For them, the hands-on argument certainly cannot be brought up. Everything I see in a room, I see via Skype. The sound quality entirely depends on your connection and equipment - I hardly experience any problems.
As usual, the rule applies: Don't judge or dismiss something you haven't tried yourself.
Edit: I used Skype for years, even before I used it for teaching, and never had a problem once. Calls are free if both parties have Skype and contact each other via their Skype account, calls do cost if you phone a mobile or landline via Skype. That doesn't mean someone might not have made a bad experience of course, but one bad experience also doth not a con artist make - stupid first or second level support employees are far more likely