No, Hugh, you're definitely onto something ....
Pings and most putters today are "heel-toe" weighted as a game-improvement design feature to alleviate the problem of off-sweetspot impact. The idea is to shift weight out of the center of the putterface to the toe and to the heel, where this weight counteracts the twisting that otherwise would occur by impacting the ball towards the toe, or towards the heel. It also tends to mitigate the loss of momentum transfer to the ball that would otherwise send the ball off a little light, with less distance than intended. The feature was a big hit with pros and golfers during the 1960s, 1970s, and 1980s, and many other putter designers now incorporate this feature. The weight distribution is accomplished in several ways -- making the toe or heel area larger; using inserts to make the middle lighter; using denser metals in the heel and toe; and other ways.
Heel-toe weighted putters typically hang at about 45 degrees when ther shaft is balanced on your fingertip. They are often called "45-degree hangers."
Putters that face the sky when you balance the shaft on your fingertip are called "face balanced" putters. These putters have a uniform distribution of weight, or at least the weight is distributed evenly about the hosel.
According to clubmaker guru Jeff Jackson in "Putter Fitting (part 2),
http://www.swingweight.com/putter_fitting2.htm:
"A putter can be “heel shafted” or “face balanced.” A heel-shafted putter has a hosel at the rearward part of the putter head. If a putter is face balanced, its face will be parallel to the ground when the shaft is balanced on your finger. A player who has a noticeable “in to in” stroke by which he takes the club back inside the target line, returns it to square at impact and then goes inside again on the follow through, will benefit by the balance of a heel shafted putter. Ben Crenshaw and Phil Mickleson putt in this manner. A player with a straight back and through stroke will benefit from a face balanced putter. Face balanced putters encourage the player to move the putter directly up and down the target line. Depending upon which way you putt, a correctly matched putter can immediately improve your putting! "
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This is the same thing Ping advises on its "Putter Fitting" page,
http://www.pinggolf.com/fitting_putters.html:
"Although a putter is usually selected based on aesthetics, putters are also designed to help golfers who prefer certain types of putting strokes. Designs can be categorized based on the balance angle of the face when the club is suspended with the shaft oriented horizontally. This angle is most influenced by the way in which the hosel or shaft is attached to the head of the putter.
The designs are described as ranging from more face-balanced, where the face of the putter points up, to more heel-shafted, where the toe points down.
Players who prefer an inside-to-square stroke, or those who tend to "pull" putts, may benefit from a heel-shafted putter like the Zing2TM, Pal2TM or Anser4TM.
Players who prefer a pendulum-type stroke, or those who tend to "push" putts, may benefit from a face-balanced putter, like the Darby or the Ally3. "
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I don't fully agree with his analysis, although it is the common one. If you read my recent tip "Stroke Path Straight or Arcing? -- BOTH!"
http://puttingzone.com/MyTips/path.html, you might agree that the so-called "in-to-in" stroke pattern is not really what happens with top putters like Crenshaw, and is not the best path for amateurs in any event. So I think "heel-toe" weighting is for golfers who have sub-optimal stroke patterns.
Once you attain a certain level of mastery with making impact on the sweetspot, the "gating" in the stroke path that "heel-toe" weighting promotes can be a bother. Pros have an average "sweetspot" for impact that is about 1/2 inch wide and just a tick below the midline on the face. Amateurs have a sweetspot that is twice as wide and just above the midline.
For some robotic comparisons of the Dandy Putter versus a handful of popular brands, check out Alan Strand's Dandy Putter site,
http://www.dandygolf.com/indexflash.htm. There are a number of side-by-side test videos. The Ping Anser sends the ball off with toe open, for example.
The question of tradeoff (bad gating versus less face twist and distance loss) for the better putters depends on a number of factors. But if the putter has a good stroke path that is designed for a face that stays square to the plane of the stroke, then the gating is more bothersome. If the golfer has pretty good contact near the sweetspot consistently, then reducing face twists from off-center hits or reducing distance loss becomes a very minor concern. In my experience, of all the problems in putting (tempo, touch, targeting, etc.), all are easier to master than making square impact on the sweetspot while the face is moving squarely thru the center of the ball. A whole book should be written only on this one topic.
So, for me, I respect golfers who choose heel-toe weighted putters, but eventually if you get to a certain level, the trade-off goes in favor of face-balanced putters. I personally prefer a face-balanced putter. You can probably make an interesting experiment by starting with a face-balanced putter and adding lead tape a little at a time to make it "slightly" heel-toe balanced, and see if there is an optimal middle-ground just for you (at your current technique and skill level) between these two basic schemes.
My Australian friend Peter O'Leary, putter maker for two decades, describes a problem with both 45-degree hangers and face-balanced putters. According to O'leary, even face-balanced putters tend to twist in the stroke because they are weighted as if hanging vertically, which ignores the reality that most putters are used with a standard lie angle of 71 degrees (19 degrees off vertical). This actual use alters the balance properties of the design. O'leary offers a simple test of this, and has instead designed what he calls "Reality Balancing" for putters. I would encourage you to read his article, "Reality Balancing -- "Face Balanced" a Golfing Myth?",
http://www.swingweight.com/reality_balanced.htm, and consider his take on the subject. O'Leary's putter, when balanced on the fingertip, hang with the toe pointing straight up. See this GolfClubReview.com review of his putter,
http://www.golfclubreview.com/drop_rb4.htm, or this one in AusGolf.com,
http://www.ausgolf.com.au/dropputters.htm. O'Leary's putter is called the Drop Putter. Alex Gamill in Texas has incorporated "Reality Balancing" in his Railgun Putter,
http://www.railgun.com/.
There is actually another kind of balancing, called "Toe Balanced." These putters hang with the toe pointed straight down. Old heel-shafted blades are often this way.
A good article about all this appears in GolfClubReview.com: ""Explanation of Putter Balancing - There are three, basic kinds of balance to a putter,"
http://www.golfclubreview.com/putter_information.htm.
The bottom line is that each putter design has slightly different performance characteristics, and if you pay close attention, you can probably putt very well with just about all of them by subtle, intelligent adjustments. In the case of toe flaring, if the putter design seems to encourage putterface opening or closing in the stroke, you can probably handle it effectively by grip pressure. I recommend a constant grip pressure at all points in the stroke, but sometimes you want a little uneveness in the pressure exerted by your thumbs down the flat of the top of the grip. If the toe tends to open going back, and that bothers you, either add a little extra grip pressure evenly in your hands or add a little extra pressure in the left thumb towards the left edge of the grip surface (to prevent opening), or both. A little adjustment like this is often all that's required to make you happy.
Cheer!
Geoff Mangum
PuttingZone
http://puttingzone.com
Golf's most advanced and comprehensive putting instruction.