As children we used to play 'kerbsie' and other games in the road. Ok there was a lot less traffic then, but we were still taught to respect the dangers and act accordingly, sweeping the ball onto the pavement when a car appeared etc. Cars also understood that kids may play in the road and drove carefully when a youngster was around. When the nearest park was across two far busier roads and a mile away, then this was an acceptable solution in quieter roads.
I like the idea of reclaiming roads as public property in certain areas. Also, I think as with the trials where roadmarkings being removed has actually improved safety by making road users think for themselves, I think this would help car drivers realise that it is not just cars that should be on the road and teaching them a long lost respect for non-drivers.