Making putts comes down to two things: line and speed. Many amateur golfers are able to get either the line or the speed right, but rarely both.
Using the follow-through drill promotes both. By eliminating backstroke, the follow-through drill forces the player to accelerate through the ball, and the line is directly dictated by the push through impact.
Getting more balls on line will allow you to dial in your speed, and the follow-through drill encourages a positive motion through impact as opposed to a deceleration.