Curryspice,
I get the impression that you are regarding cycling as 'recreational' and therefore 'optional'. I am sure that I am not alone in wanting my children to be able to use their bicycles as a main mode of transport - far better than me taking them by car on shorter journeys.
The majority of their journeys (Cubs / Scouts / ballet / football / cricket / school / into and back from the centre of town) are between 0.5 and 4 miles - the shorter ones are conveniently walkable but the longer ones are not within the time constraints available.
There are no cycle paths.
The 'quiet side streets' are in fact by far the most dangerous on their routes - they are lined on both sides by parked cars, and moving cars dodge their way down at 30 miles an hour leaving no space for a cyclist between the moving and stationary vehicles. At least the main roads, even where the traffic is faster, have space for a car to pull out round a cyclist.
Since my kids learned to ride bikes confidently (between 4 and 5.5 years old) we have been 'training' them. Initially, they cycled in parks etc - and learned there that they had to stop for pedestrians coming the other way, and walk round a pedestrian if going the same way. Then, they cycled with me on the pavement (yes, you read that right - I cycled on the pavement with my children. Went into the police station to find out whether that was acceptable, and was told that as I was accompanying very young children on roads where I could not cycle on the road as I would be separated from the children by a row of parked cars, that was not only acceptable but also something they would recommend). Same rules as before for pedestrians.
Then me on road, them on pavement. Same rules for pedestrians.
Then all of us on the road as long as an adult accompanies them.
DS (10) will do his cycling proficiency in school next year and I will then allow him to cycle independently on the roads BECAUSE I HAVE SPENT 7 YEARS TRAING HIM TO DO SO SAFELY. Part of that training has had to be with him on the pavement. A child cannot go straight from 'learning to ride' to 'riding on the road' in most towns and cities, and therefore the carefully-monitored, pedestrian-friendly, use of the pavement during the training period is essential during the training period. Pedestrain awareness and courtesy during the training period is in fact good training for all kinds of road courtesy later on.