Everything is within a system. I'm not sure how you can separate out the effects of gear, instruction, terrain, etc. That said, I feel grooming is a big part of it. On a well groomed slope it takes little skill to go faster then you can "safely" crash. As evidence consider Mad River Glen. 60 years of operation, Gnarly terrain, not a lot of grooming, 0 fatalities from ski crash related trauma.
As to the stickers.....
Where I used to teach we had a ton of school groups. We would have 75-200 4th-6th graders every week day. We would team teach in stations. As the kids would "master" a skill they would be sent to the next station. After a run on the beginner chair we would mark thier ticket.
If they didn't have a mark they had to be with an instructor to ride a lift.
If they had the mark they could ski all day on the beginner lift.
They had to have a mark AND an adult chaparone to go anywhere else at the resort.
Worked well for many years, then the lawyers found out. We were then told we were not allowed to mark tickets because that was evidence that we said they could ski, which meant if they got hurt skiing it was our fault for giving them permission.
It was fun showing up after the "graders" left. If you didn't know if the schools had been there you would look up the beginner hill from the office. If they had been there there would be a scraped off track, left turn at the top of the lift, straight down, left turn back on to the lift. We used to joke about how much time we could save by not bothering teaching a right turn.