Roger I think you are a pretty good example of a street rider who illustrates from their own experience that counter steering is so much easier to use and control than weight shifting and you don't seem to be confused about using it. It's a simple process that is easier to teach and learn than body position/weight shifting.
There is also something to be said and enjoyed by those who use weight shifting to steer although I don't think they fully understand what happens when they do it, but regardless if that works for them and they don't care to learn another way, they should keep doing what works for them.
Those who favor weight shifting over counter steering street bikes, for the most part, counter steer through a corner and recover to straight regardless of how the the lean is initiated. I have heard they think for heavy bikes counter steer is good, but not for all bikes. I would agree to a certain point. I have never argued that a bike cannot be turned (eventually) by weight shifting, however counter steering works on all street bikes with the same amount of ease. It doesn't take shifting the body and/or loading weight on the inside peg and against the tank with the outside leg. The rider can sit center and go with the forces of the bike without strain, by simply counter steering, big bike, little bike, heavy bike, light bike, or any size driver (within reason).
I don't deny that some riders on some bikes can successfully make their selected bike turn in the corner of their choice at their selected speed without touching the grips by weight shifting. I would like to some day ride with them on my streets so they could convince me how effective their method is!
I would agree that many riders, probably most, have started riding without the knowledge of counter steering. Most/many probably have ridden a bicycle and transition to motorcycles without a lot of turmoil. That doesn't prove that counter steering is complex or that we should just go out and ride to learn the hard way. What it proves is we have done a terrible job at helping new riders better control the motorcycle, especially during challenging events like avoiding contact with other obstacles and contact with the ground other than with our tires and feet!
I do know their are street riders that perform well by using a combination of weight shifting and counter steering that they enjoy and are competent, safe and smooth.