Dear Matt,
That's a question I've been thinking a fair piece about lately, and I'm glad you asked it. You're right about the feeling, but there's kind of a way to have the good feeling and the low putterhead too.
First, you have to have a stable setup so that you know in your body exactly how far it is from your eyes and the pivot of your stroke at the base of your neck down to the ground. Once this setup is established, your putter ought to be in your grip with the combination that lets your hands and arms hang very heavy and dead under your shoulders, but the bottom of the putter does not rest on or get pushed down onto the green. Instead, the bottom of the putter is poised on the tips of the grass blades, bending them but not crushing or folding them. That way, with grass mow heights just above 1/8th inch, your putter's sole ought to be about this high off the turf itself.
That's pretty "low" or close to the turf, so you would "stub" the putter either going back or coming thru UNLESS you are careful about holding the pivot at the same height (and not letting the pivot sink any lower AT ALL) and avoid upper-torso "sway" where the pivot moves laterally back and forward with your stroke motion. The "sway" invariably is not truly lateral only, but involves a little downward dipping. So, to be safe, and to simplify the stroke, manage the pivot in the base of the neck so that nothing goes lower or sways.
The only other way to "stub" the putter is to allow the putterhead to creep farther from your pivot in the course of the stroke. This happens mostly without the golfer being aware of the "opening" of the elbows during the stroke. That is, at setup, the arms are not really hanging all the way, so there remains a mild crook in each elbow. This is typically caused by golfers using too long a putter, or even if they have too long a putter, not getting their hands low enough on the handle to start with. So, regardless of your putter's length, always hang the arms and hands below the shoulders FIRST before adopting your grip on the handle. This gets the crook out of the elbows.
If the crook stays in the elbows, some golfers are OK about keeping the "triangle" of their stroke setup intact during the stroke, but even these golfers get snakebit when unmindful of this point or under pressure. It is practically impossible to notice the elbows slipping open in the stroke because you are so concerned with more important matters; and due to the small range over which the elbows actually open, the sensors in the elbows don't pay much attention or yell at your brain about it.
So, altogether, it is best to hang your arms and hands ALL THE WAY that gravity will pull them, without "sticking" them down with muscle tension. The hang needs to be relaxed, but heavy. Once the hands are down, if you crook your wrists downward like a fly fisherman in casting short casts, this position of the wrists sticks a little "safety" tension in the forearm that stabilizes the elbows and helps keep them from "wandering open" in the stroke.
Once this setup is established, you should be able to use only your wrists and waggle the sole of the putter 3-4 inches back and forth over the tips of the grass like lightly brushing the grass. If you placed two nickels in a stack on the green and stroked across them at this setup, you ought to be able to knock the top nickel down the line. Try a dime also. This shows you that the pivot height is the key to making the stroke return to impact with a low putterhead -- about as low as you dare go.
Now, when you make the stroke, if your stroke is a pendulum stroke, the main idea is to keep the butt of the putter aimed to the centerline of your body as you turn back and thru. How much curvature up or back around in the backstroke (and reversing on the thrustroke) depends at this point on how your upper torso is positioned above the ball. If you stand a bit tallish, the putterhead will rise a little higher than it does if you are more bent down to the ball. The closer your upper back and arms look like a giant L over the ball, the less rising of the putterhead. But it's only a matter of degree either way.
What happens in the thrustroke is that taller-standing golfers like Crenshaw are dealing BOTH with some rising of the putter after impact and the putterhead path curling back around the body (to the inside). Because the putter actually stays in contact with the ball briefly (and a little longer with slow tempo and a soft-insert face), it is necessary to keep the putterhead headed square for several inches during impact. This is something contrary to what happens naturally from the tallish setup, so these golfers have to inject a conscious move to keep the putterhead headed down the line. To do that, the left or lead elbow has to avoid curling back towards the hip and instead move straight along the toeline parallel to the puttline. The end result is that it "feels" like "extending" the putterhead out away from you a bit. This has been "interpreted" as "keeping the putterhead low thru impact."
Part of the feeling is also from the fact that the pivot does not sway. If you sway in the upper torso area going back, your dipping left shoulder makes the pivot sink a little and move backwards laterally a little. This "tilt" of the head that results makes you "feel" that the putterhead is rising quite a bit. It may be rising some, but not all that much. So golfers have interpreted their habit of keeping the pivot still and making it "feel" like the putterhead is staying low going back and then coming thru. The same is true of golfers with the upper torso bend lower to the ball, but not as noticeably so.
All of the above describes a "low" putterhead for golfers who use "dead hands" and keep the triangle intact. There are plenty of golfers who change their wrists during the stroke. Tom Kite used to set his hands at address cocked forward a bit, angling the shaft toward the hole, like a preset forward press. Dave Stockton uses a forward press and Phil Mickelson used to, although he seems to have changed lately. Loren Roberts allows his right wrist to fold going to the top of the backstroke and the freezes that angle for the rest of the stroke down and thru.
The effect of all these manipulations is to deloft the putterface and present less "dynamic" loft at impact than is built into the putter. Combined with moving the lead elbow straight along the toeline instead of allowing it to curl back inside toward the hip then REALLY "feels" like keeping the putterhead low thru impact. But it's not really -- it's keeping the hands lower than they would be without the elbow move.
So, to sum it up, what you want is to hang your arms and hands fully and relaxedly, adopt your grip so the putter is poised above the turf and brushing the tips of the grass blades, and keep the pivot stable and the triangle intact as you move the putterhead back and thru. Then, when the lead elbow stays online past impact, it will feel like you are keeping the putterhead low going thru.
Also, this move depends a little bit on how forward in your tsance you play the ball. I recommend playing the ball about two inches (or even two and one-half) ahead of the center of your body and the bottom of your stroke arc. So even though the putterhead "feels" like you are staying low thru the impact area, you really don't want to try to keep the putterhead "level" at the same height all along from, say, four inches behind the ball to six inches in front of the ball. "Level" and "low" are two different things. Just be satisfied with keeping the hands low during the stroke so the hands stay the same distance from the base of the neck or chest at all times, and forget about going for a "level" blow. This way, ball position and low hands combine so that the putterhead is rising slightly past the center of your stance, and the end result is that you "send" the ball off rolling with a nice soft kiss-thump with the lower half of the putterface, not a pop or a slide. This is normally what gives the ball a good rolling start and keeps your tempo nice and smooth.
The follow-thru needs to feel like you're in control, and that's because of the elbow. Allowing the hands to creep higher means the elbows are "closing" in the follow-thru (bending shut). This is because your upper arms are getting involved in whacking the ball with "hit" and the upper-arm muscles tug the elbows shut -- like a little jerk on a suitcase handle. So, again, "low hands" and relaxed arms avoid this, too. The feeling of the follow-thru is mostly about tempo -- how the thru-stroke mirror-matches the speed pattern of the backstroke and how -- like the backstroke -- the putter swings beneath the neck and coasts to a stop smoothly. The smoothness and completeness of the thru-stroke is what you are after, with low hands and an elbow move.
Let me know about your experience with this advice. I don't want to overwhelm anyone with complicated baloney!
Cheers!
Geoff Mangum
The PuttingZone.com
http://puttingzone.com
Advanced putting instruction from the world's most comprehensive resource.