If you are assigned a group for the week, and teach most of the same group for the week, you aren't escaping for a request, and should be embarrassed for thinking you should.
Some instructors refuse, or make it known that they would prefer not to teach young children, or less accomplished adults. It is those skiers who will return for the next 6 - 10 years that keep you on skis.
A resort has to keep as many people happy as possible, and most ski school directors will make up any personal loss of requests many times over because they appreciate what it took to be requested in the first place.
As recently as 5 years ago, I directed a ski school that taught 400 lessons an hour.
We researched instructor compensation to insure that we were at, or above the norm. Many eastern schools were paying a percentage; however, requested privates were not a large part of their business.
Destination resorts that teach more than 70% privates cannot comfortably pay a percentage, as much of the income from the lesson is used for overhead. If they do pay a percentage, then many other forms of compensation are set aside. One example is pay for showing up. Resorts that pay a percentage are unlikely to pay you just to be available. Some resorts paying a percentage do not give adequate discounts for meals. Many resorts that don't pay a percentage have an employee cafeteria, where the savings are significant. Finally, percentages do not fairly compensate long time instructors vs. less experienced instructors, unless the percentages are scaled. The math in the scale rarely works out for the long time instructor.