As a nanny i always use reins and if parents don't, I usually ask them if i can and I explain that i want to ensure their beloved child's safety and have my own sets of body reins.
In my opinion reins are a freedom for children and a way to bring up stranger danger and enviromental dangers.
On a trip to America in 2002 with 3 children 3m, 2.3yrs & 3.9yrs [ looked after them since 1st was 6m], the sight of the older 2 walking along side the pushchair with their reins on drew comments, 1 mum stopped to chat and made it clear she thought it was not 'on', funnily enough after she went on her way the oldest one commented that 'her ds was likely to get lost as he didn't listen to his mummy!'
Needless to say a few days later said mum was hysterical, ds had run off in the shopping mall, it was pure luck that the oldest spotted him, and held his hand [no way was i going to touch him] as we backtracked to his mother, she was very keen to ask where she could get her own set--walmart i replied, not exactly thick on the ground in Beverly Hills.
I get my charges used to reins well before they are mobile by using them in the pushchair. The 2 oldest often walked ahead of my in the park linked together by their reins and holding hands very happy and feeling safe and secure.
As a side benefit it is easier to prevent a new walker falling over as tho you may lose grip on their little hand when they trip, you have the reins and are able to pull up on the reins to avoid an accident
I feel it is the safest option in the current climate of stranger danger.