I've wondered about these things ever since I lived in the UK. I wonder what goes on in the mind of the person who buys and displays one of these things. Do they, for example, assume that if they do NOT have this sign in the back window, their baby is in more danger? Is having this sign somehow making them safer? If so, it follows that they also assume that not having the sign up in the rear window somehow makes their journey more dangerous. So...it also follows then, that they believe that without the sign in the window, following drivers take less care to avoid a collision with them...which in turn requires an assumption that drivers normally don't really care too much if they hit the car in front of them.
It all seems very silly to me, and is a classic example of an item which really serves no purpose being sold to customers with limited intelligence in order to offer an illusion of greater safety. What MIGHT work is if the sign said 'Nitroglycerin on board' or 'Thermonuclear device with hair trigger on board'. I'd take some notice of that (I'd want to be heading in the opposite direction) for sure! But really, 'Baby On Board!'?
The really interesting part about this morning's encounter was that despite displaying this sign in the back to keep nasty other people (in this case, me) from ruthlessly slamming into the back of her car (as I would otherwise have done just for the hell of it, obviously), the youngish woman in the drivers seat was very obviously using her cell phone in text mode as she was stationary at the stop sign, and again as she was driving along. I suppose that fits nicely into my theory about the IQ of people who buy and use these signs.
I'm seriously thinking of designing and selling a 'Middle aged curmudgeon with lots of aches and pains on board!' sign - any takers?