"That's the reason I noticed it, because we've got one on the way as well."
An NZ Transport Agency spokesman confirmed young children did not need to be kept in child restraint seats when travelling in taxis, shuttles or buses, according to the country's traffic laws.
"However, where a safety belt is available, the child must be restrained, and where an approved child restraint is available, it must be used (where appropriate for the child's age and weight)," the laws state.
"Taxi companies may provide child restraints if you give them 24 hours' notice."
The spokesman said the Transport Agency advised people travelling with young children to contact taxi or other passenger service companies early to request a car with a child restraint.
Taxi Federation executive director John Hart understood the concerns but said it wasn't practical for taxis to store child safety seats in their cars.
"I understand people's concerns but I don't really know what the answer is," he said.
He said most boots weren't big enough to accommodate luggage and child seats.
It was also not easy for taxis to pop back to base on short notice when they get an order for a customer wanting a child safety seat.
He said parents often brought their own safety seats along with them when catching taxis.
Automobile Association road safety spokesman Dylan Thomsen said that sadly the situation in the video was not a unique case.
"Most children are put in appropriate capsules or kid's seats but a number aren't and that puts them at a lot more risk if something goes wrong on the road," he said.
"No parent would ever want their child to be hurt but people can totally underestimate the forces involved in a moving vehicle and think it will be alright.
"It doesn't even require a crash. If a driver had to slam on their brakes in an emergency it would be very hard to hold on to a child and keep them safe."
He said the AA pleaded with all parents and those driving with kids in the car to not take unnecessary risks.
Kids needed to be in a appropriate capsule or seat in the back seat, he said.
"Small children can't make these choices themselves so it's up to us as adults to keep them as safe as possible."