Who is going to install and remove the seats every time someone calls for one? Are they going to have liability insurance in case they accidentally install a seat improperly and a kid is injured or dies?
And then the parents have to go back and make sure the seat is clean once they're done with the car. Kids are amazing at finding ways of making messes when you least expect it.
I think "have young kids" is one of the ares where the "car as a service" concept does not work. Not unless you drive only very rarely with the kids.