It's pretty telling that in many countries (e.g. the EU), child seat laws are relaxed in taxis. It's an acknowledgement that there can be a tradeoff between safety and convenience.
If it's OK to hold your child in the backseat of a taxi to the airport, why shouldn't it be OK to hold your child in the backseat of your friends' car on the way to the airport?
My guess would be that it's a question of numbers. You want 99% of kids to be in child seats, and can allow a few exceptions (since e.g. nobody does a commute to daycare in a taxi). But if you allowed private drivers to avoid car seats in limited circumstances, people would abuse that privilege and never use a car seat, turning that number down to 70% or lower
There is no fundamental "why". Sometimes a law only needs to get you 90% of the way to an ideal to satisfy legislators. We live our lives steeped in such procedural gaps, but to live any other way would probably become a micro-managed nightmare.
In theory, a taxi driver is a trained professional (like an airplane pilot) whose safety record, attentiveness etc is much higher than the average driver. In practice, probably not so much.
But when it comes to driving it doesn't really matter much because half the accidents involving two cars are someone else's fault.
I'm not sure if fault is that binary. Sometimes, you're right, the other driver is at fault and there is nothing you could do. But often, you can drive defensively in a way that protects you from even serious mistakes by others.
I have personally not been in far more accidents than I've been in just because one of the two parties was paying attention and took the correct evasive action. Sometimes that was me, sometimes it was someone else. This is only the cases I've noticed, there were probably times where I did something stupid and didn't realize it, and the other person took evasive action anyway, or even cases where I took the evasive action without noting the other person did something stupid.
We need to look out for each other. Nobody is perfect, but the better each individual does the better the whole is.
If it's OK to hold your child in the backseat of a taxi to the airport, why shouldn't it be OK to hold your child in the backseat of your friends' car on the way to the airport?
My guess would be that it's a question of numbers. You want 99% of kids to be in child seats, and can allow a few exceptions (since e.g. nobody does a commute to daycare in a taxi). But if you allowed private drivers to avoid car seats in limited circumstances, people would abuse that privilege and never use a car seat, turning that number down to 70% or lower