Carrying a fire extinguisher in a car is likely to be counterproductive and dangerous.
Modern cars contain many materials that are highly inflammable, and in some cases very toxic. Recent videos of car fire demonstrate just how quickly fires in cars can spread. The only safe thing to do if your car goes on fire is to get all passengers out and abandon the car as quickly as possible. Attempting to fight the car fire with a small fire extinguisher is foolish and dangerous.
It is therefore unwise even to carry a fire extinguisher in a car in case some drivers might be tempted to fight the fire.
In a video of a recent car fire in Cork, one could see that the Cork fire brigade personnel who responded, wisely and professionally, did not attempt to fight the fire until after the fuel tank had exploded, and then approached the car wearing full breathing apparatus.
In situations like this, it’s best to save the people not the car.