Every Wednesday evening, my friends 10 yr old son does a paper route that is just under 2 Km long. At this time of the year, that means working mostly in the dark and along streets that are pretty bare. It's supposed to be his older brothers route, but the elder got sick of it and was going to quit. The younger lad campaigned heavily for parental permission to sub-contract the job. (Since the newspaper company wouldn't hire anyone younger than 12) He's been doing it for a little over two years now with no problems except for one jerk who usually has a hostile and aggressive acting dog. The man tells the boy to just ignore the dog, to tell it to shut up and go on with his delivery. Both my friend and I have told the lad that controlling this dog is NOT his job. If there is any doubt, any cause for concern *whatsoever* he is to skip the delivery and let the jerk complain to the newspaper.
When I was a child in the major city of Toronto, two of my friends and I routinely made bicycle trips that were well over 3 Km in round trip length so we could explore a ravine city park/conservation area. Plenty of opportunity to get into an accident, get lost or encounter a person of bad intent. Lots of adventures, some minor accidents scrambling around in the ravine, but NO tragedies.
we moved when I was 11 and for the remainder of the school year (about 4 mths IIRC) I escorted my 5 yr old brother on the TTC to our old neighbourhood, dropped him off at the day care and then proceeded to my school around the corner. Our mother went with us for the first trip, just to reassure herself that I knew the route as well as I claimed. (a short bus ride to the station, several stops on the subway and then a 4 block walk above ground) But after that, it was all on me. The following year, it was a 1 Km streetcar ride, followed by a two block walk for my brother and I to attend school. His afternoon day care picked him up at lunch time, but after school I picked him up from daycare and took him home. We usually walked because there was a bakery we would mooch day old goodies from. I took care of my brother until our mom got home at around 5:30.
TL'DR version. Both my own extensive experiences at that age and my daily observation of kids that age today suggest that a 1 mile walk from a park IS NO BIG DEAL. It really does depend on the competence of the child(ren) involved and the character of the route being taken.