Better to just crank the bindings so they never come off. Kids bones bend, not break. (Usually).
IMO the biggest problem in teaching kids to ski is too soon, too hard, too much. If they need the leash they're not ready. If they're in the back seat they're scared and the run is too steep for them. I've seen too many dads taking kids down runs that were obviously way too hard. It turns them off skiing, it makes them worse skiers, not better. I've seen dads screaming at their kids to hurry up on a powder day. Too much family drama in the parking lot. It's great for the kids to have fun in the snow at any age, but they don't need real ski gear or a lift ticket to do that. At most--cheap toy skis that strap onto snow boots. I'm not talking about waiting until puberty for real skiing--toilet trained should do it, like I said before. The hard part about teaching kids to ski is finding time to ski yourself, unless you have the money for ski school or ski day care.
That said, plenty of people did the opposite of everything I said and the kids turned into great, passionate skiers.