I guess it's a complicated answer. I am interested in neurology and psychology, and my job involves analyzing what conditions people need to learn a new skill.
A common misconception is that the brain and body are separate. They are integral to one another. This is obvious when you think about it, but people forget all the time.
A person who has been static for a while, perhaps looking at text on a screen, has a lot of brain activity in some areas and very little in others. Not integrated. He may be tense in his shoulders and breathing shallow, unaware of his body carrying stress. He is more likely to react defensively in fight, flight, or freeze to any change in his environment. Now imagine him driving home in this state. Imagine he carries this state home to his wife and child. He didn't sleep well, and he goes to work again. He's in a bad mood and can't make his mind focus.
Maybe he tries some music to help him focus. Maybe meditation. Strong coffee. Maybe he goes for a walk. Any of these can be helpful, but they still largely ignore that the brain lives within a body.
We know that moving in three-dimensional space (like rolling/ukemi), challenging core postural muscles, and having physical contact with people produces massive shifts in attention, emotional regulation, and learning. That is brain integration. The smooth transmission of information from sensory neuron to action potential. Most people don't even know it exists, and they don't try to maintain it.
RE: What your not being told about traditional martial arts and mma