For expats moving to Vietnam, getting around is always a worrying issue. For us peasants who don't have a company car and who can't afford a private car, there's little other option. But it's not all bad.
It must be understood that transport in Vietnam still relies heavily on two wheels. Public transport is poor and unsafe and only the wealthy can afford cars. If the family wants to take a trip then the motorbike is by far the most convenient and cost-effective means, and for the vast majority, the only choice. Yes, it can be seen as dangerous, but Vietnam is still a poor country where the standard of living is below that of what we might be used to in 'the west' (or what we were used to, see Greece, UK in a few years).
Upon arrival in South East Asia the sight of children, toddlers and even new born babies on a motorbike is shocking. I'd agree, it's not great, particularly in Saigon's inner center, not least because of the traffic but also the horrible fumes which can't be great for young lungs. But it needs to be understood that most Vietnamese parents are not being reckless and take as many safety measures as possible when travelling with their children. There are those cases you see where there is recklessness, allowing toddlers to stand up on the seat, riding without a helmet, driving too fast - but these are the minority.
There is also the context of the journey to consider. I take my daughter on the motorbike, but only out in Phu My Hung, very rarely on longer journeys. If we need to travel into the city or beyond we'll take a taxi - thankfully, we can afford that. Also, whenever driving with Louisa, I drive with extra caution. Some might say that doesn't make a difference, but I feel it certainly cuts the odds a great deal. I also feel in complete control whilst driving with her around my local streets - I would never take her on Highway 1A with articulated lorries thundering past.
So for those with children considering transport issues I would ask firstly do you have an alternative (car with driver, taking taxis everywhere) and secondly do you feel comfortable driving with your child on your motorbike?