A lot of time is spent talking about clubhead speed. There are a couple of ways to create clubhead speed. A bigger swing is very effective because it gives you a bigger arc to build up clubhead speed or a more efficient way is using torque which creates a tremendous amount of clubhead speed.
As a boxer in the military, I learned to harness my power more efficiently by using my body instead of my arms. If a boxer relies on their arms, they will punch themselves out. However, by using my body I created more power behind my punches and I was doing it more efficiently. I was able to defeat boxers who were much bigger because they relied on their long arms to generate power while I was able to harness more power by getting my body behind each punch.
Now apply that to a golf swing. You can either make a bigger swing with your arms to create clubhead speed or you can use torque through resistance and create more clubhead speed more efficiently.
A single plane swing turns the arms, shoulders, chest and hips on the back swing. Timing of all these components is difficult at best. When done correctly it generates a lot of power. It takes a lot of practice to develop the timing to synchronize the hips, chest, shoulders and arms. Most recreational golfers don't have the time to spend on developing the timing needed for this type of golf swing.
A two plane swing only uses the arms, shoulders and chest on the back swing. Resistance is created when the chest, shoulders and arms turn while the lower body resists. Torque builds up in the lower back, latisimus muscles and abdomen. On the down swing, power is unleashed as the chest begins to turn the shoulders and the arms follow.
The goal is for the impact position to mirror the set up position with everything square at impact. Golfers using a single plane swing typically have an impact position with the hips already rotating past square forcing the chest, shoulders and arms to catch up. If the timing is off, a golfer could either be open at impact causing a slice or because the arms are trying to catch up with the lower body a golfer could over rotate and be closed at impact causing a hook.
A two plane swing hinges the wrist early then turns the chest, shoulders and arms while keeping the hips square to the ball so that on the down swing the chest, shoulders and arms return to their square set up position at impact. The result is hitting the ball square at impact with more power. The hips then turn through the ball on the follow through by getting the heel of the rear foot up and perpendicular to the ground. The ability to hold the finish position until the ball lands demonstrates great balance.
In a single plane swing, the arms are trying to catch up to the hips causing a tendency to change tempo on the down swing. Tempo is easier to maintain throughout the golf swing using a two plane swing because the hips remain square on the back swing allowing the chest, shoulders and arms to square up at impact with minimal effort.
For recreational golfers, the two plane swing requires less practice to become proficient and generates more power. It keeps it super simple (KISS)!