Controversial perspective but I think that cycling is a lot more complacent about the risk of accidents than, say, rugby. "That's the sport".
Ds has just been involved in 3 days (4 stages) of cycling at the Youth Tour of Scotland (girls ranging in age from 12-16 and boys 14-16). 80 boys and c60 girls on closed roads in Perthshire. In that respect, British Cycling is good cos it insists on closed roads for youth cycling.
However in 3 days cycling, for the boys' races along there were 3 ambulances (one very complex forearm fracture, one broken leg (so ds told me) (1st lap and last lap of Race 1) and I'm not sure what the injury was in Race 3 (race 2 was a shirt team time trial). Narrow roads, mud, water, lots of potholes.
At previous Youth Tours in England I've seen many more ambulances. Kids get knocked out and get back on their bikes and race the following day. 
Rugby (ds' other sport) is considered a "dangerous" sport - yet if we had that number of ambulances at rugby games/festivals, we'd be doing something very wrong. I don't watch a rugby game with my heart in my mouth, yet I breath a sigh of relief when ds finishes a cycle race. 
Yet when we raise concerns, we're told "That's what the pros do".
I love the cycling community and the other parents are great but some of the attitudes to safety by some not all of the organisers is antideluvian. 