The goals of such kind of training session is to develope consistancy with a given excersise.
Your coach is trying to send you balls with consistant spin, at the same angle and on the same place so you can find the way to return the ball consistently with the required tecnnique. The gooses necked wrist helps you keep the blade on a fixed position and easier feel and find the appropriate angle and move. If your wrist is loose, without the appropriate technique you will give to the ball different spin, angle and direction with every return and your coach will not return to you consistent balls - the excersise fails and you can't develope. So listen to the coach, if you have hasitations just ask him.
About the goose and the style - once you develope persistant skills, you may start to polish your style tuning in your way the different elements of the archtecture of a technique.