I'm still not convinced countersteering is ever necessary since it is obviously possible to lean a bicycle without turning the handle bars at all. Why wouldn't lean first then turn the way you are turning work? Or even lean while turning the direction you want to go. I am slow in general and for me most turns are sharp and low speed.
Any kind of serious turning involves lateral acceleration. The bike must lean (well, the centre of gravity must be offset laterally from the wheels contact patches) to compensate. It's an inverted pendulum, with a feedback mechanism (caster angle of the forks) and the combined effects of gravity and centrifugal force (from the rider's perspective). There are also minor secondary things like gyroscopic effect of the spinning wheels.
The equilibrium position (lean angle) of this feedback system can be shifted by the rider either by applying force to the handlebars, or shifting the centre of mass away from the middle (leaning your body to the side).
It's possible to steer by only shifting weight, but a bike with locked handlebars would not stay upright (no feedback mechanism). Applying force to the handlebars is the way to get maximum control authority over the system.
Edit: more detail... the tilt angle is defined by the lateral offset between the centre of mass and the wheel contact patch. The rider shifting his weight achieves this by moving the centre of mass, while using the handlebars moves the wheels to the side while leaving the centre of mass (mostly) unmoved. Of course, the wheels' contact patch can be moved further and faster laterally (by steering) than the rider's weight can be shifted (which is limited by the rider's flexibility).
Sounds like you are agreeing with me then? I'm not saying no handlebars at all, just that if you want to turn right it doesn't seem to actually be necessary to slightly move the handlebars left first, which is the claim that is often made when this discussion happens.
I agree it's possible in principle to ride a bike without the handlebars (have done this myself on many occasions, including motorbikes), but more dynamic maneuvers do require use of the bars (e.g. swerving to avoid an obstacle).
Sudden maneuvers are an essential survival skill on two wheels, and it's important to understand how to steer rapidly. A rider who just steers intuitively is vulnerable to a phenomenon known as "target fixation": becoming mentally focused on an obstacle and steering into it. Having a rational understanding of how to steer allows the rider to exert conscious control over the bike's direction in these situations.
