You're Correct!

In the putting stroke, keeping your left wrist firm is a must. The putting stroke is an action that should be dominated by the bigger muscles in your upper body, mainly the shoulders and the arms, rather than the smallest muscles in the hands and the wrists being used to create power.

As the putting stroke is more of a finesse action of great control, if you try to create the power with your hands and your wrists then you will be very inconsistent, not only in the quality of the impact on the putter face but also in the distance control of your putts.

To make sure that the left wrist doesnt break down during your putting stroke, you have to try to maintain the Y you form between your forearms and the shaft of the putter at address. To do this you need to make sure that you are holding the putter more in the palm of your left hand and not in the fingers. Next you need to make sure that you are directing your putter both in the back stroke and the through stroke with the bigger muscles of the shoulders, rocking the pendulum motion back and through. In your minds eye, see the left wrist staying flat, the back of your left hand moving away from the ball and then moving through to the target.

You can practice this by taking your set up position. Once you feel comfortable, take your right hand off the putter and place it behind your back. Start your shoulders rocking in the pendulum motion of your usual putting stroke. Feel the left arm moving with the shoulder motion so the putter moves on a natural arc back and through. Now hit some putts from between two and three feet in this way and see how many you can hole. Once this starts to feel comfortable, make some practise strokes with your right hand back on the handle. Make sure you feel the same dominance and firmness in the left wrist as you did when your right hand was behind your back.

Whether you have a putt of 10 feet or 100 feet, the way that your hands work particularly the left wrist throughout your putting stroke should remain exactly the same. The only way to gain consistency with longer distances is to increase the length of your back stroke and not to let the left wrist break down.

Power is one of the last things that you need to create during your putting stroke. If you try to flick the putter head with your hands you will only succeed in losing control of the distance of the putt and potentially have the putter face in the wrong direction at impact.

If both of your wrists move freely throughout your putting stroke, the bigger muscles, i.e the shoulders that you need to create a controlled pendulum motion will not be allowed to function correctly. Not only will you struggle to hit your putts along your intended aim line, but you will also struggle to hole out from short distance consistently too.