I am also of a mixed mind, not regarding children's needs for freedom, but just how that plays out in my life. And I'm becoming seriously weary of how often I also have to tell my children that we do xyz because other people are uncomfortable if we don't/might think they are not being cared for and remove them from our home and family, etc...
We live in the woods, and in bear country. For this reason, we have a large range with a bright blue string tied tree-to-tree to mark the perimeter of the area that I feel comfortable about them being without supervision. We have no fences and our three oldest play outside around the cabin and to the markers all day with a window open for me to hear them. We also have geese, who I trust to provide an advanced warning system, unless they were to hide instead- there's no real telling what they'd do if faced with a grizzly or black bear or cougar.
Anyway, it's usually in town where we have all of these manufactured rules about walking proximity and wandering ranges. In the deli, ds1 wandered around out of sight for a long while once he'd finished eating and i still was. At the park, all of my dc go in whatever directions they choose, and I do keep a closer eye on our 20 mo. old, but even he is often at the other end of the playground.
For the youngest, the most common problem is when others try to stop him from doing what he is competent or willing to risk doing. I don't climb with him or hover unless he's asked me to, which is next to never unless the challenge is completely new to him.
If we had a dog, I don't think I would be even as concerned about safety as I barely am now.

I would let the three older ones wander with the dog, but this is a very rural area with dirt roads and not a city.
*I* feel tense in the city, and so do my dc. We're just not used to the pace of the city, but even so, I am happy to let them run a block ahead, from light to light.
My biggest concern about the city is that while I rust my dc, people in general aren't anticipating children even being there like they did when I was a child. In parking lots, it is imperative that I have all of their hands because drivers simply are not looking for their little bodies way down there. They see me, though. In the streets which here are very pedestrian-friendly and even in stores, my dc are commonly nearly knocked over by fast-moving, unaware people whose gaze simply doesn't meet the little people. My dc have not been knocked over because they are very adept at maneuvering their bodies to avoid it, but the adults are clearly not aware and when they become aware, after near-misses, they apologise to me, surprised by having such a close encounter with a little one. I see this all the time.
I don't think that's reason to hole up, though, just something to consider and maybe remedy with fluorescent orange hats.

I was extremely free-range as a child, in many diverse neighbourhoods and cities in Canada, and lots of dangerous things happened to me, injurious to this day. I do wish my parents had been more aware and concerned for my safety. They didn't consider the environment or my needs. If I said that I was afraid to walk home in the dark, they said I'd be fine. I wasn't always. I was also taught to suppress my instincts. Bad combo, imo.
So, my solution is to assess the environment, my child's abilities and desires, encourage their instinctual development and awareness, help them strategise and work through things as they want my help, and otherwise, to let them learn, which I think they are innately competent to do.
Our children wander further away as they are comfortable, just like when they were babies. They have a sense of how far is too far, I think, except the 20 mo. old presently- or maybe it is just me... hard to tell...

We also equip them with observations in situations they haven't encountered, like at the family park day we happened across on the weekend. We just pointed to a few things so they'd be aware of their presence. Then they ran about the various tents and activities and I stayed with our 20 mo. old while he wandered over to listen to the music in the front row.
When it was time to go, the three oldest all knew where the others were, even though they'd gone in different directions, and we gathered and left together.
I am learning how to apply my understanding and being open to our dc's expressions of needs and desires every day, and this aspect of being together seems to be in constant flux too, according to our situation.
I guess I just anticipate that we'll all adapt to whatever we need to, and given that we're making a conscious effort to meet one another's needs, even if I miss some and mess up some, and some more, my dc will have learned well enough what they need to go around me if I'm the obstacle- though I'd rather never be that!
I hope to be more like a lighthouse they can rely on to be there when they want to come home. Always there, always welcoming and indicating a safe and warm place to be, and to leave as desired. I try to be that in everything and everywhere for them.

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