ZWExton most people routinely miss the exact center of the putter on many putts. Longer putts tend to cause an even bigger miss. Over the years, a large part of putter design has been trying to decrease the effect of these slightly missed strikes.
My MacGregor had an insert that is softest in the center and increasingly firm moving outward in either direction. Distance control is really good with this feature. The new Cleveland putters use different milling on different parts of the face to create the same advantage.
So the problem is much more prevalent than you think it is. I'd wager that if we had ultra slo-mo video of every out you took during the course of the round, you would be unpleasantly surprised by what you saw.