The no brakes exercise is merely there to help the rider sharpen and develop their sense of speed, once the first two sessions are done with no brakes, we WANT the rider to use the brakes in the corners where slowing is necessary. Yes some riders have trouble over-slowing so some options in that instance are: apply less pressure at the braking point, or perhaps move the braking marker further into the turn (which can be scary sometimes). Trailing the brakes gives the rider the luxury of extending the braking zone further into the turn and gives an opportunity to adjust the speed to precisely what the rider was intending. There are other uses for trailing but that's one important aspect.
Some public roads have long series of corners that are all about the same speed, therefore not requiring much braking. But when slowing is needed, go to the brakes even if lightly. You'll have the lever in your hand in case something suddenly appears you need to brake for as well.