Holly has hated being in her pushchair since she learned to walk, and will hold my hand most of the time but has a bit of a tendency to wiggle free and run.
To me, her safety and happiness is paramount. So we use a 'leash' (I don't like that word, she isn't a dog). It means that when we go out anywhere, she has the freedom to walk at her own pace, stop and look at things, wave at people, run her hands along the walls. Yes, it takes us hours to walk anywhere, but she loves it!
I would rather she be on reins and happy (and safe) than in a pushchair and miserable, sat there not getting any exercise. I do not use them to drag her along, I use them to give her independence whilst making sure she is safe. And I can assure you that neither I, nor my baby, are 'chavvy'.