I worry that a leash might give the child a false sense of security. I always keep an eye on my kids, but I also teach them to keep an eye on me. Being on a leash would be teaching them that it's safe for them to bolt or just go in any direction and rely on me to pull them back or redirect them. I really don't want to do that.
I also think using a leash is lazy parenting sometimes. Either keep your eyes on your kid, or stay in places where your kid will be safe. Of course there are exceptions and special circumstances, but for a trip to the grocery store or a walk in the park? No, I wouldn't ever have considered wearing one, even when I had two under 2 and my oldest DD was a bolter. I kept an eye on her, and when we were in a dangerous place, like on the side of a road, I made her hold on to the handle of the stroller or shopping cart or hold my hand.
And about the degrading vs. not degrading debate: what would you say if you saw an adult with special needs on a leash? Would that be okay? Because if not, then why is it okay to put one on a toddler?
To me, it's not about the childs or the person with cognitive difficulties' perception, it's about the signals that we send to other people. How can we expect people to respect childrens rights and treat them as individuals, if we send out a not-so-subtle signal to society at large that kids are just like dogs to be kept on a leash?
I sort of get the false sense of security thing, although the use of a leash doesn't mean you're going to let your kid pull you with it and be wild. It can definitely be used as a training tool for learning how to hold hands and stay close, which I think is great.
As for not being a lazy parent and "keeping an eye" on your kid, an eye is not going to stop your kid from running into the street unless you are some kind of wizard. If your daughter would hold your hand or hold onto the stroller handle when asked, she was not a bolter. Bolters don't hold things and stay close, they bolt when you least expect it, in a parking lot, or a crowded airport. That's why they are called bolters. In my opinion, good parenting happens when you care more about the safety of your child than the message you are worried about sending others.
And again, exactly how is a leash worse than strapping a kid in a stroller? How would you feel if you saw a special needs adult, who could walk, strapped into a stroller?