Here is my thought on the whole kid riding deal. There are a few "factors" to me.
No offense to anyone on the board, but far too often I see "my bike fell over in the garage", "I high sided going 20 - 30 mph", "granny pulled out in front of me and I ran off the road" kind of posts all the time on here. Accidents do happen and are often unavoidable. However, 95% of these kinds of posts are from people who have very very little riding experience and they immediately go out and buy a bike. If you are new to riding, a 600 can be the death of you real fast, let alone the king of the world busa. Your brain is all you have on a motorcycle, use it, far ahead of time.
My daughter is 13 and has been riding with me since she was around 5 to 6. The only concern you have from their standpoint is feeling their little helmet hit your back because they have fallen asleep riding. That happens to all kids, it relaxes them to hear the noise. That is a concern, plain and simple.
I have been riding since I was 3 years old on go karts and started at 4 years old on cycles. I am now 35 and have had probably 75 bikes ranging from dirt bikes, harleys, to sport/hyper bikes. I was for a period of a few years, a professionally licensed AMA supercross/motocross racer. I am as confident on my bike as I am brushing my teeth in the morning.
If you are a very experienced rider, you are putting your child in no more danger than you are driving them to school in the morning in a car. If you are a novice of < 5 years, that is a judgment call. Ask yourself, "what would I do if bambi ran out in front of me?" things like that. If you can't answer immediately, then you are not ready.
I have had more crap like that happen to me than I could tell you, yet I have only had one accident on a street bike and it had to do with two factors. 1) me following too close, 2) the dip**** slamming on their brakes so hard they went from 45 mph to about 2mph in the span of 3 seconds. A bike doesn't stop that fast and it sure don't help when I grabbed a handful of front brake and did an endo
When I am riding, I constantly scan as far possible down the road anywhere I go to see if "grandma" is pulling out of her driveway, kids are playing in the front yard that might run out in front of you, pot holes in the road, broken pavement in the road, etc. You HAVE to do this or you are asking for trouble. You don't ride on the far outside lane in a curve, not in the middle, nor on the far right side near the edge of the road either. Yellow lines, built up oil in the middle of the lane, and the pebbles on the right hand side will have you on your ass quicker than you can call the insurance company.
Bottom line, if you don't jump on that bike when you ride it and know you are in 100% control, then practice riding some more until you do.
Ride safe
My daughter rides a 600 on the track.
My son has no bike interest. 
she does, but she's 18.
