Let me provide some points from the management perspective (I'll probably put myself in hot water here, but so what).
Every ski area in the country either own or lease their land so despite the thought that they are on public lands, they do have a legal right to restrict what activities occur. Case in point, this is why Burton, or for that matter the whole snowboard industry, has not tried to sue for access to Mad River, Deer Valley, and Alta (the 3 remaining resorts to not allow snowboarding).
Almost every ski area in the country provides a free season pass as a benefit for working there. Many argue that you need the pass to work so it is not a benefit, but I have heard that Deer Valley has gone around that by providing passes on days when instructors are working and if they don't work they have to go to their manager to see if they can stay on the hill (Deer Valley does restrict the number of skiers per day that can visit so if they are sold out and somehow you are not working, well your headed to PC or Canyons for the day if you want to ski).
Every ski area in the country carries the liability insurance that covers the ski instructor. I have, personally, looked into personal liability insurance and it is not cheap especially for a "high-risk" activity like skiing.
My last point, at least at my area, we provide a lot of free hours of training to our staff. They don't have to pay, but the ski school does pay the trainers (who are also the highest paid instructors) so there is another benefit cost. You could also start to factor in other benefits like, at my area, passes for family, food discounts, retail location discounts, many equipment companies will only sell, at pro form, to ski school staff, worker's comp if injured while working, locker room space, free parking (yes this is a benefit at some areas), free tuning equipment and wax and I'm sure we could all think of a lot of other stuff.
Then there is the marketing question. Was it really your stellar instruction that drew the client to the resort in the first place, or did they come because of another reason?
All of this adds up to a lot of upfront cost that instructors don't have to deal with. And I don't know an instructor out there that isn't taking advantage of almost every benefit they get, it's how we afford it. The biggest factor, for me, is the liability. I just don't think it is worth it nor do I think I could get paid as well.
Does off the books happen, sure. I could name 3 people at my area, not affiliated with the ski school, who give private lessons. The smart ones only teach kids and pawn it off as babysitting with a little skiing. Really the impact is so little, especailly with a kids ski school the regularly sells out, that we don't give it much mind. I can name a few part-time staff members who teach off the books to clients they have had forever and it annoys me, but I have bigger fish to fry. I, myself, have skied with staff from other ski schools, at my mountain, for a burger and a beer trade.
As I always like to say, this is just my perspective.