Surely its the other way around. It's reasonable to expect all adults to wear a seatbelt in a taxi but not reasonable to expect all taxis to carry child seats. It wouldn't be unusual to expect on occasion for a parent to travel with 3-3 children; should all taxis therefore carry 3 child seats? No. Should all adults travelling in taxis use a seatbelt when one is available and required when travelling in private transport? Surely yes.
I wonder how much extra you could charge for having a vehicle in the uber fleet with a variety of child seats, or similarly various handicapped accessories.
Why? It would be a major hassle otherwise when visiting cities like SF or NYC if you are not planning to rent a car (if you are, you might be carrying a car seat). I wouldn't be comfortable using a random carseat in the trunk, and in any case, given different age kids require different carseats, it's not really feasible.
Would you be more comfortable using none than using a "random one in the trunk"? I do not really see how a carseat can cause additional harm in an accident.
This is just so fundamentally disconnected from anything I can relate with I don't know what to say. I'm all about being critical of "safety first", sometimes to the chagrin of my wife, but having or even requiring child seats is not bubble wrapping. (though I do find the "until they're 9" in California a bit much)
