I have 3 kids 5,7,8 and biking is our primary form of transportation. (Only one car, and my wife has a long commute, so 5 days of the week we are carless even if we wanted it.)
The transition has been pretty smooth. In ~2 years my older two have gone from barely able to doing 5 miles to doing 10-15 easily, and we recent did 20. My 8 year old understands more rules of the road than most drivers.
For my littlest, we did a trailer for a while, but as soon as he was big enough we moved to a trail-a-bike as my panniers have more than enough capacity for most trips. When needed, however, we'll even do trail-a-bike and trailer in a long train.
Every kid is different, but I think many parents are way too cautious about pushing their kids into biking. I've consistently been surprised at how capable my kids are, almost always underestimating them.