A child leash has a fundamentally different structure than a dog leash, but serves a similar purpose; Kids need to be kept near at hand and under observation at all times when in public spaces for their own safety. Dogs, likewise, need to be kept on leash because off leash it is very easy for them to become seriously injured, killed, or lost.

I find the leash preferable to strapping the child in to a carrier or stroller because it gives the child some autonomy while still protecting the child. The child is free to walk alongside you, look around, interact with things near them, and generally do kid stuff while being kept within sight and within a safe distance. It strikes a balance between control and freedom, giving the kid autonomy that they might not otherwise be able to have. For instance, if the parent or caregiver has to carry bags or other items they cannot hold the child's hand and would have to confine the child in some way for their safety. The leash, then, allows the child more freedom and agency than would otherwise be possible.