You're Correct!

If you want to be a consistent putter you need to keep your wrists out of the stroke. Rather than creating your power from the wrist, you need to use the triangle of the arms and shoulders that you create at address.

By creating a rocking motion of your shoulders, you will start to move your putter in a pendulum like motion, almost like the pendulum of a grandfather clock ticking back and forth.

Using your shoulders and arms will help you achieve a better path with your putter and eliminate the possibility of your putter head wobbling about in the backstroke especially. This is essential for you to consistently start your putts on your intended line. Take your putter and stand in front of a mirror and check the following points:

Set up looking face on into the mirror. Take care to make sure that your arms are hanging straight so your elbows are not bent.
Whilst looking into the mirror, make a slow, smooth stroke making sure the only moving part is the shoulders gently rocking. It should look like your left shoulder rocks a little down in the backstroke and then a little up in the through stroke.
Turn your body so you can see the putter face and make the same motion. Now you will be able to see the consistent path the putter is taking as you make your stroke. If you have the room, hit some putts toward the mirror and you will see the ball rolling nice and true every time.

The only real exception to the rule would be if you had a putt of considerable length or if you were putting from off the green through the fringe or the apron. Here is where you need to feel that your grip pressure is a little less firm so your wrists feel ‘soft’. This will give you the slightest movement from the wrists to help you hit the putt the required distance whilst maintaining control of your stroke.

You don’t need to use your wrists even if your putt has to travel up a tier in the green. Using your wrists will see you either hit your putt too soft and the ball won’t get to the top of the tier and end up back by your feet, or you’ll hit it way too hard and you will race your putt far beyond the hole. Watch the majority of the tour players on TV and you will see how they increase the length of their backstroke to take into account the severity of the slope that their putt needs to travel up.

No matter how slow the greens are, having a putting stroke that has wrist movement will not help you. Having a putter with more weight in the head will help you maintain your distance control on the slower greens.

Golfers with a stroke that always uses the wrists to move the putter will struggle for consistency with putts of all angles and distances. Not being able to judge how far your ball is going to travel, whether it is from two feet or 20 feet, can then lead into all kinds of other issues from decelerating to the dreaded yips!