Always start them on a blue (or blue-black) slope, because it forces them to learn to use the edge of the board. Lot of easy drills like side slipping and simply turning your head to control direction.
If you start a snow boarder on a green run, it always results in them catching an edge and eventually face planting. Not a fun experience.
Surely you can't be serious?
Obviously can't start them on a slope with moguls, but it needs to be a steeper slope that forces learning how to use the edges.
The slope rating is different between resorts. A blue at Arapahoe Basin is likely a blue-black at most others which is why I made that distinction.
Once they learn to properly use their edge, and commit to using it, they will progress quite rapidly.
After that, it's just about fitness and the risks that you're willing to take.
great analogy!
Likewise, music. The most popular method -- Suzuki -- starts kids out without sheet music. Reading comes later.
In both cases, it's also just less gear to manage. The benefit becomes obvious in group lessons and recitals.