I live in Germany and six year old children get trams to school by themselves. My friend's five year old does (with her big brother, and she's been using that route with a parent for two years). People would think you ridiculously overprotective for insisting on holding a (NT) eight year old's hand. If anything the roads are more dangerous here - a huge metal tram cannot stop quickly and often the drivers are high up and wouldn't see a small child who ran out suddenly.
We lived in England when he was younger, but I didn't have a car so he had to learn road sense and safety at a very early age. I took a pushchair pretty much everywhere even after he started walking reliably and the rule was that if he couldn't walk sensibly we held hands, if he wouldn't hold hands he went into the pushchair. I stopped using the pushchair when he started nursery at 3 because by then he was reliably stopping at roads. He has never once ever run out into a road and is now 6. I don't hold his hand now unless he's tired and wants to hold mine, or if we're crossing a tricky or particularly busy road. He's been using a scooter in the street since about 4 and always knew the rule was that he had to stay in sight, must stop at corners and road crossings and he has to get off the scooter and walk across the road. If he did not follow this then he was not allowed to ride the scooter. We were very lucky to live around very quiet streets, so he got a lot of practice of the rules without any real danger, and we talk regularly about not going on the road even if your balloon/ball/toy/teddy/animal/anything at all goes on the road, he has to stop and ask an adult to get it for him and understand that it might not always be possible for them to do that. He does this - he's been upset about it, yes, especially when he lost a conker and the conker immediately got squashed by a car! But he didn't for a second try to go after it, and he was quite nervous about me trying to get one back as well when he saw a car coming from far down the road.
I did try reins but he used to sit down in the middle of the street randomly which was a pain in the arse. There were a couple of times when he was a toddler that he would hold hands to cross the road but then suddenly go limp in the middle of it and I ended up picking him up by his wrist (ouch!!) because I had a buggy in the other hand! Anyway they all go through phases but if you're consistent about the rules then they get the message in the end. I don't think you can say that there's a particular age that children are safe to walk unconstrained, cross roads etc, it's all down to the individual child and the parent's judgement. I would always say err on the side of caution
It is harder for children to judge speed and distance as they are lower down but if you teach them to only use proper crossings and to be extremely careful where they can't find crossings (which should only be on quiet roads anyway) then there's not really any reason to worry about that.