maxinc

Counter steering is explained so that you become aware and apply a certain amount of control to what your mind already does. Essentially, you can not lean a 2 wheel vehicle above a certain (low) speed without counter steering. We learned counter steering when we were kids and got started on the bicycle.

As for going too hot into a corner, there are quite a few other things just as important as conscious counter steering. It starts with learning to approach the corner at the right speed in the correct position, learning to fight destructive instincts such as chopping the throttle or breaking while leaned over, lifting your vision by looking at the exit point, keeping a positive throttle to increase traction on the rear wheel, move more body weight inside the corner to make the bike more upright and stable and a some other details thought trough advanced training and track time.

You can read about this stuff for free on the internet. Practicing them until they become second nature takes a lot more time than the regular riding school allocates for the DSA test.