As in many other sports, the only people who get much fitness training while participating in the sport are the beginners. As a person becomes proficient at the sport, the less energy is needed or expended. Inexperienced fighters are always moving (usually the wrong direction that requires they move even more). They execute numerous attacks (not precise attacks to specific targets) and they react rather than anticipate. When you watch experienced fighters fight, many of which are older masters with pot guts, they do very little. They have years of knowledge, experience, and skill and are able to be at the right place at the right time with the right techniques. They anticipate attacks and are ready for them. Therefore, they do not need speed and a high level of fitness, since they do not expend much energy.
I once competed in Judo against a blind black belt. I thought I would take it easy and not make him look bad, but instead, I was fighting for my life and trying to save my pride. He seemed to read my mind. When I tried to attack, he stopped it before I could get it into motion. Sometimes, he would even say something like “An ippon seionage (one arm should throw) will not work” before I had even begun the attack. It was spooky. At the end, I was wasted and he was ready for the next opponent.
While I was stationed at the naval base in Iceland, a student of mine pointed out the base handball champion. He was an old, fat guy who chain smoked and waddled similar to a duck when he walked. I did not believe the student so I went to watch a handball tournament. While the younger players ran back and forth, reaching for balls, and bouncing off the walls, this guy just waited in center court and the instant the opponent swung at the racket at the ball (before it even made contact), he waddled into position and waited for the ball to arrive and then hit the ball back to the opponent’s far side. This guy could read the opponent’s intention from his swing, knew the exact trajectory the ball would take while bouncing off the surfaces, and took action before the ball was even hit. I have seen martial arts masters embarrass younger students in the same manner.