I have seen this happen many times in sport: Science could not find the value, so coaches simply cut things out prematurely.

Cooling down after a workout is as important as warming up. It's when I know that I'm almost done after an intense workout and I feel a lot better too! On the other hand, we still need to permanently remove many approaches from training, as they are mainly risky and ineffective.

Cutting out or truncating cool-downs just because we don’t fully understand them is a bad idea. A cool-down provides the body with a smooth transition from exercise back to a steady state of rest.
Cool down is normally associated with aerobic exercise, like running, biking, stair stepping, elliptical, swimming, etc. But did you know that most people forget or even skip this part? Cooling down after exercise allows your muscles to adapt to a new less-stressful motion. Cool down. A cool down means you are …

This means if you stop too fast, you could pass out or feel sick. Actually, these processes depend on the intensity of the exercise developed before, could be a jog or a walk, also stretching can be used.

Here are some important benefits to a cool down and what a cool down can consist of.
I know this because I see it every time when I'm at a gym or when I teach a group fitness class. Cooling down are low intensity exercises to permit the body to reduce stress into a resting state. After physical activity, your heart is still beating faster than normal, your body temperature is higher and your blood vessels are dilated. What consists of a cool down? It is important to cool down after exercise so that you do not hurt yourself. Why Cool Down Is Important and You Should Do It After Exercise.