Your car has side mirrors to help show you the picture to the side and rear, so why should you bother changing things when you are towing?
Your side mirrors give you a restricted view of the area to the side and rear quarter of your car. Usually, this is adjusted so that you can see part of the car in those mirrors. This gives you some perspective so you know where you are actually looking at. The side mirrors are designed to fit on and show the view from a car.
Once you are towing, your whole perspective changes. You are no longer driving a car, but a truck or even a tractor and trailer rig. The length of your combined vehicle will be twice if not three times what it was. Your old mirrors will not do. Even with adjustment, they will be showing you a good picture of what you are towing. They will not be covering a large enough area or giving you a picture which is far enough back.
When you move out in your car, you have a feel for the speed and acceleration you can achieve and the distances involved. In your towing scenario, all that changes and what you need to see changes too. You need to see further back and have a wider view. You are otherwise at severe risk of pulling out or changing lanes by moving into someone else’s path. You are an accident waiting to happen.
The aim of the towing mirror is to give you that extra width and depth of vision, so increasing your safety and that of those around you. For that reason, in many areas it is illegal not to have one if what you are towing is wider that what you are driving.