This is mostly copied from my reply to another comment:
Parents get tired. In fact, most parents have chronic levels of sleep deprivation which impairs things like concentration, reflexes, ability to pay attention, etc. Then you have parents who might be working multiple jobs, be dealing with health issues that affect sleep, etc. A leash would make that job to keep kids safe much easier.
No leash equals a non-abusive, even though not every situation can allow a parent to keep 100% focus on the child, but using a leash the parent suddenly becomes abusive?
Should a parent not give the kid a helmet when learning to ride a bike then also? Does using a helmet mean the parent is abusive?
I just don't understand this. I cannot fathom that someone would criticize a thing that objectively and provably make life in the world safer for children. It's just another tool to help kids get to grow up.
There are countless stories of children just walking away in the 3 to 5 seconds a parent looks away where the child falls off a height, falls into water (not every parent can swim, and not all waters are swimable), gets picked up by a stranger in a crowd, etc. Situations that a leash would 100% have saved the child's life.
And when these people are confronted on why it's abusive or "embarrassing for the child", they don't have an answer.
They might say something out of left field like "children aren't dogs!", to which I say "yes, you're right. Children aren't dogs. Very good! Now about the leash, why is it abusive?"