Well, I see why someone wouldn't want to pay for a service first, and then risk not getting it. From the other side though, how many times had I clients that would schedule, then ditch at the last minute. You get several of those who frequently do that, you aren't getting any money out of them, AND you're putting huge holes in your schedule that other, paying clients coudl fill.
My stylist, mechanic, doctor, even local dog-groomers require a deposit now, and if you cancel within a time-frame, still owe the money. To top that off, if you re-schedule, you're billed an additional $25.
A lot of scheduling problems and "unforseeable circumstances" can be boiled down to courtesy and common sense. The true accidents that DO happen DO take care of themselves because of their nature.
Due to the nature of dance lessons, people think that dance teachers sit around the studio all day waiting for people to show up, and don't have lives outside the studio (although, if you're a secondary/tertiary teacher in a chain studio, that's true, likely). They get taken advantage of more than doctors, mechanics, and other "necessary people" in the workforce, because they're taken seriously on the floor as an instructor, but not as a human with a life and groceries to shop for.