First you don't need to close the trail to set up a simple NASTAR type paneled slalom that you can ski on virtually any type of skis, The terrain parks are open to the public and far more dangerous than a simple dozen gate NASTAR type course. You also do not need timing. Any coach or instructor can set a 20 second paneled slalom course in 10 minutes. My point, if you watch our U12 racers many of them carve and have much better control than the average recreational skier. Ride up the chairlift and the majority of recreational skiers do not even generate turn shape. They just ski straight with a check turn here and there, That's why I believe using gates to create turn shape among recreational skiers taking ski lessons would go a long way to improve their skiing.
Terrain parks, though 'open', have an access gate or similar, and signage regarding potential hazards, S.M.A.R.T. protocols, etc... and is maintained by a dedicated paid crew.
Gates set by race groups on 'ooen to the public' slopes are marked by signage, and monitored by a coach at the top and bottom of the set. Other areas locally have a dedidicated hill or pitch, and will be roped off along the length to keep public from straying into the course.
There's time, effort, and risk management (read liability) protocals in setting gates or making terrain features. And yes, while gates are wonderful, it's costs money, time, and personnel to set, monitor, and maintain, which is why most ski schools don't, or can't afford to set them.
We do use cones, carrots, pylons, and tunnels in our learning area though, but it's very difficult to do elsewhere on the mtn for all the reasons listed above.