I have to take a little different tack here:
I recall keeping my middle child on a tether (some might call it a leash, it consisted of a loop around his wrist, closed by velcro with the same on my wrist, connected by a coil of plastic wire).
We used it only out in large crowds. I remember using it specifically when we used to go to summertime evening concerts, you know what I mean, come early, sit on the lawn and picnic and then listen to the music once the sun goes down.
From my perspective it allowed him more freedom to go exploring in the bushes, chattering with other people, etc. yet I know exactly where he was and I had complete control of his whereabouts.
I don’t think he was embarrassed or has suffered any blows to his esteem.
We got a comment occasionally but the kid seemed to enjoy not having to hold my hand all the time as he wandered around in the crowd.
My perspective anyway.
SRM