I feel a bit free-rangey, age appropriately. My son is nearly four, our backyard is fenced in and gated so he can't get out, and I let him play in the backyard and sandbox while I work in the kitchen (which looks out onto the backyard. If I'm working out in the front garden, he can play in the side or back yards.
I think it's healthy for him to have a little space, to not feel so very watched-over constantly. At parks and outings, I look for safe ways for him to have a chance to walk on his own, near me but not next to me, on his own path. I've taken care of children for nearly 20 years and have very good judgment regarding this. I'm also extremely vigilant when this happens, because he's so young, and am constantly checking for bikes, dogs, and others so that we can be considerate of those we are sharing the park with.
I think you've got it right, personally. More kids fall into swimming pools, die in car accidents, or have severe injuries due to not wearing helmets. Stranger danger is WAY blown out of proportion. It's a familiar face that's more likely to be a predator to one's child. We don't stop driving, or keep our kids off bikes (although our house rule is No Helmet-- No Wheels), or stop buying kiddie pools.
I don't condone it, but starting in first grade, I was getting to school on my own. Back then, I had to cross twice at a busy intersection (I was 5, almost 6 then); in later years I either rode the bus or walked 6-10 blocks to school before I was even 10. I rode around the neighborhood alone at 12, 13...
I also took plane rides and bus rides (Greyhound) unaccompanied, since I was about 10 or so. I felt proud of being able to do this 'alone', even if there were flight attendants keeping an eye out and making sure I got to the proper gate and on the plane. Those were the days....
I think unsupervised play is about being age-appropriate to the child's level of ability (to negotiate, to think clearly when upset, to make right choices most of the time). Your daughter sounds like she's at an age where she can demonstrate those characteristics. My son isn't yet, but when he's old enough and does show me he's capable, he will be allowed more freedom.
Great question!
H.