Stuff has this article on deaths and injuries from farm bikes. Headed, provocatively, "A New Zealand Death" written by Charlie Mitchell. It is worth a read. The reason why it caught my attention - apart from a natural interest in the morbid arising from working in life insurance - was that a friend's son has recently suffered terrible injuries in just such an accident. He has a broken arm and badly broken leg. The photos looked a lot like the ones in this article.
I will not jump to the conclusion that these deaths are preventable by a law change, or that quad bikes are inherently unsafe. 33 deaths were recorded from these causes in a period of about 10 years. Although many more injuries are likely to have occurred - the article hazards a guess at 20 times as many. It is worth contemplating how many equivalent injuries and deaths would occur by letting a child use an ordinary motorbike, or ride a horse, for that matter. Risks are real and they are also the stuff of life. I have let my kids do similarly dangerous things - parents cannot keep children's lives entirely risk free without taking something else away from their lives.
But it is also worth wondering how many could be prevented by requiring a roll cage be fitted to the four wheel versions of these vehicles. I hope someone is pondering the questions, because the list at the end of the article is heartbreaking.