When I was a kid, seeing toddlers on reins was a normal thing. It was just how it was in the 60s (which I am too young to remember) and the 70s.
Recently, while in town, I have seen several toddlers with a wristband on, possibly velcroed on, and a curly lead thing which then goes to a wristband on the parent. Is this the sort of lead that you mean?
I guess it eliminates having to hold the child's all the time, although I cannot see hand holding as much of a hardship. Perhaps its to stop them getting lost in busy pedestrain shopping areas, or in the shops themselves.