Something something Burt Ward.
I’ve always assumed other drivers were, like me, trying to avoid collisions.
But if somewhere out the roads there are crazy drivers looking to intentionally hit other cars, I figure a “baby on board” sign would just make you a more attractive target for them.
Some of those stick figures are funny. I especially like the one with the chainsaw wielding figure, standing over a bunch of stick figure body parts. 
The first ones had suction cups, and so could be removed. But that was obviously too much trouble.
Since this was a consumer fad, that fact that it is a stupid idea is not an argument against it being for emergencies. It is not like it was officially mandated or anything. And while your scenario is okay as far as it goes, relatively few cars in an accident explode into a ball of flame - outside of movies, that is.
I certainly don’t get the argument that it was to keep people from crashing into you. It is not like people usually pick who they crash into, even if they were in a spot where they could see the sign.
Today they are totally useless since the person crashing is probably texting anyway, and is not going to notice anything.
We have neither a baby nor a car, so no. But you do see those occasionally over here. Except one Thai couple decided to take it to the next level and had it painted on the back of their car. Except they weren’t quite proficient in English, because their sign read: “Baby on the Board.”
Quartz: You probably don’t know the real story behind Baby on Board signs
The Wall Street Journal: After the One-Hit Wonder
Until a few minutes ago, I really thought the purpose was to inform first-responders that they should be looking for a baby in case of a wreck or a fire. And I thought that people who had the signs permanently mounted on the car were endangering first-responders who were looking for non-existent babies in burning cars. And I was sure Oprah had something to do with it.
But I guess I was wrong. A man named Michael Lerner started marketing the signs in 1984. He got the idea after driving his nephew home and fearing for the nephew’s safety on a road filled with aggressive drivers. He bought the idea from a pair of sisters who saw the signs in Europe, but unsuccessfully tried to market them in the US.
I’ve always thought if the people with the baby on board signs were serious, they’d take the signs down when the baby isn’t on board. Otherwise, I think they’re bad parents for leaving their baby in the car in the dead of night or when it’s below zero in the winter.
My favorite of the parody signs: Caution! I drive like you do!
I didn’t know those signs were serious. I thought…I don’t know what I thought, because nothing else actually makes sense, but I guess I assumed they were some ironic statement about babies or maybe some old cultural reference I wasn’t getting.
I honestly don’t think I’ve seen one since the 80s or maybe early 90s. And recently I’ve been looking for them out of idle curiosity as to whether anyone still had them. All I see these days is those stick figure family decals.
I think it’s just a form of boasting, or assuming everyone else is going to be as obsessed about your baby as you are.
I think the drivers are just gloating that they are intelligent enough to have figured out how to reproduce.
Damn you! I wanted to make that joke.
Now I’m wondering if there’s a market for a Burt Ward baby-on-board-style sign.
Sadly I cannot find the video for ‘Baby on bumper’. Maybe HBO still regulates the copyright.
The very first ones (ca 1984) I saw were removable - there was a hook affixed to the rear glass and the sign hung on it.
Yes, the cover story was to alert first responders to look for a baby.
Reality: We just got the latest Yuppie bauble! Eat your hearts out, you barren losers!
Oh great now I got that Homer Simpson and the B-Sharps song stuck in my head :o)
My impression was that it was simply a consumer fad, fed by all sorts of urban legends.
For example, I was once told, with a straight face, that such signs were a legal requirement for parents driving with babies. This no doubt fueled by the ‘official, standard’ look of the sign.
Another rumour - that first responders have to take some sort of action based on the sign (that gets repeated upthread).
I don’t think it was a ‘boasting’ thing primarily, but rather, a ‘mistaken safety/conformity’ thing.
I never used one, not seeing any point. Though it may, as Marge Simpson said, have “stopped people from intentionally ramming our car”. 
Fuck no.
I see them around, but I’ve never had the slightest urge to own one.
I think, though, that some people just really like telling the world about themselves. I’ve always seen the ‘Baby on Board’ stickers as being like the ones that say ‘I Heart My Breed of Dog’ or show some sports team. It’s just another bit of random personal info that the driver needs to share.
No, not a ‘Baby on Board’ sign.
On the other hand, I’ve always wanted to put this in back window:
BABY-BOOMER ON BOARD