My oldest is incredibly independent and as soon as he started walking, that was the end of staying with mommy. (He got out of the house once without me knowing and crossed the street to go play at the neighbor's house. He wasn't quite 2. Worst day of my life.)
He's a big boy, so carrying him was out of the question and stroller's aren't always convenient, like in the airport while dragging luggage, or trying to grocery shop when you've got a baby in the seat already.
So we turned to the leash and I loved it. He loved it, too, because it meant he didn't have to sit and could run off some energy.
We didn't use it for long... maybe a couple months... because I started specifically taking him places to practice being obedient. We'd go to the grocery store and I'd hook the leash to the cart and he'd have to hold onto it. He could let go when we were stopped, but when we walked, he had to hold on. We did that at the zoo and anywhere else that it was crowded. Soon that evolved into not having to hold on, but knowing he had to stay close. Now he's 2 1/2 and does really well.
I don't ever remember seeing any nasty looks, but I wouldn't have cared if I'd gotten any because it obviously meant they didn't understand because they'd never lost a small child and didn't know the absolute terror of going through that. I had nightmares for weeks and it threw me into labor. (Yep - 38 weeks pregnant, running around the neighborhood in a panic. Not cool.)