All good reasons but, the most important use for the rudder when you are learning is to speed recovery from an unwanted inverted position. A student's most common error is the right hand turn towards himself. The result is a plane that is usually nose down with a 120 degree or greater bank. The classic entry into the dreaded death spiral. Most trainers have fairly slow response on the ailerons. This is good when you want time to "think" through a manuver. But when time and altitude is running low you need to apply rudder also. The best way I've found to demonstrate the difference to students is to teach them to roll the plane with both aileron and rudder. Once they see the increase in roll rate they understand the effect the rudder has on the plane. From the first flight encourage them to use a little rudder when rolling the plane. Once you understand the use and the effect of the rudder the easier it is to introduce cross control or torque neutralizing applications.

Another good reason that trainers should be tail draggers. Then from the first flight the student would understand the effect of rudder application.

I just thought of one more exercise. Trim the plane to fly straight and level at 50 to 60% throttle. Then have the student fly with rudder and throttle only. Rudder for directional control and power for altitude.