If you do not keep your left wrist firm during your putting action and you flick your wrists as you strike through impact, then you are not making a pendulum action with your putter and this will result in a lack of consistency, distance control and accuracy.
If you consider how a pendulum swings, the top of the pendulum is fixed in position and all of the pendulum swings as one unit below this, at a constant speed and tempo. There is no hinging action half way down the pendulum, the pendulum swings from the upper part of it. Applying this to your putting stroke, the upper part of the pendulum is your shoulders, with the bottom part being the putter head. To move this pendulum, you need to swing from your shoulders (as the fixed or anchored upper point) and ensure that the pendulum of your arms and the putter remain as one unit. If you flick your wrists during your putting action, then you are introducing a hinge half way down the pendulum.
One issue with this is that the putter head will not swing at a constant tempo or rhythm. As you make the flicking action, the putter head will speed up and this will hit the ball at a higher tempo making distance control difficult to achieve. Swinging without this hinging action at your wrists will result in a more constant tempo and with this smoother action you will obtain more consistent distance control by using your swing length to dictate the distance that the ball travels.
The second issue that flicking your wrists causes is that the putter head will be rising as it strikes the ball. When this happens and you are connecting with the upper part of the golf ball, it will again affect the distance that the golf ball is hit. The bottom of the putter face striking the upper part of the golf ball will result in a much shorter putt than the centre of the putter face striking the side of the golf ball.
The flicking action will also cause you directional issues as when you hinge at your wrists the putter face will turn left of the target and the putter head will also travel left of the target line, making it difficult to strike the ball along the intended target line.
The cause of flicking your wrists as you putt is being too dominant with your right hand, if you are a right handed golfer and vice versa if you are a left handed golfer. To cure this problem and to create a more pendulum like swing from your shoulders, you need to reduce the influence that your dominant right hand has over the putter.
When you set up to play a putt, in simple terms you create a “Y” shape with your arms and the putter. If you are making a pendulum action putting stroke you will swing this “Y” shape back and through the ball, keeping it intact and controlling the movement of the “Y” shape from your shoulders.
A great drill to help you achieve this and to keep your wrists much more passive during your stroke is to hold lower down on the handle than usual, so that you have three or four inches of the putter handle above your top hand. Place a golf ball between your left wrist and the handle and swing the putter back and forth without dropping the ball.
If you flick your wrist and become dominant with your right hand, you will increase the gap between your left wrist and the putter handle and as a result you will drop the ball that has been placed there. This will instantly provide you with evidence that you have flicked your wrist. Work on holing putts on the practice putting green without dropping the ball that you have positioned between your left wrist and the putter handle. You will now be swinging in much more of a pendulum action and be controlling the movement from your shoulders.