Even in the early 80's Chuck Knox was called a dinosaur for featuring a run first offense.
Ball control is a good strategy. No matter if it's quick dump off like in the WCO or power running. Moving the chains rests the defense and puts pressure on opposing defenses. The rewards of running the ball usually surface in the 4th quarter when defenses get nicked or tired. Just think of how many big runs Lynch had late in games.
What occurs to me is that defensive backs seldom miss plays and aren't rotated much. Receivers are regularly rotated or rested for plays they aren't needed in. As the game goes on, DBs get worn down more than receivers. If you can keep the opponents defense out on the field longer the big pass game opens up in the 4th.
I'll second and third this. Ball control and defense are the BEST way to win games.
If you can't control the ball you can't stop the other team from scoring, and every game turns into a track meet where whomever scores last, wins.
If you can control the ball then you can burn the clock while you lead, and open it up when you're behind. Either way, your opponent is always under pressure to take risks to keep scoring points because they can't blow you out, but you can blow them out. Risks lead to turnovers and more opportunities for your offense.
Belichick, Payton, Tomlin, Harbaugh, Carroll all know this. That's why they've been so successful over the years.