Former driving instructor here. Here are two phrases I used to use regularly on lessons:
Children + wheels = huge danger. (Scooters, bikes etc; once upon a time it would also have been roller skates, or pogo sticks according to the Ladybird books of the 70s and 80's!)
Children + ball = huge danger. If they drop or kick the ball into the road, they're likely to go and get it. Even now, I drive extremely carefully past children who are kicking a ball as they walk along.
I also used to say "that walking iPod might keep walking across that side road". "Does she have headphones on under that hood?" "With black clothes being so fashionable, it's hard to see pedestrians in the dark; all you can see are the reflective bits on their trainers." "Runners don't like to stop for any reason on Earth."
Also dogs are unpredictable, even on leads. I recently alarmed my parents by driving practically on to the other side of the road to give a dog on the pavement a wide berth, as you might overtake a cyclist: said dog was on a long lead, on a narrow pavement. I had checked there was no oncoming traffic!
There's another thing not often mentioned: because children are smaller than adults, to the driver it looks (at first glance) as if they're further away.
Having said all that, I remember being allowed to run ahead aged 6 (not on main roads), being allowed to go to places on my own aged ten, so that I could manage walking to secondary school, across several busy roads. I agree with some previous posters that excessive hand-holding can be counter-productive, and later they wouldn't be able to decide for themselves. My parents used to say things like "we'll cross after that white car", or "after which car shall we go?"
I know this thread is not about learner drivers, but as an instructor I met some 17-year-old learners who looked as if they had never crossed a road independently in their lives, and found it very difficult to judge speed of cars, and to make decisions. I've seen instructors of child cycling groups getting an army of children to turn right in front of oncoming traffic, calling out to them "make your own decisions, guys."