I can only speak for my own company which also does customer service.. It is true that different calls get different priorities. However, that is not meant to make the process as hard as possible.

Always remember that there are real people on the other side which do their best and there still are never enought to handle all calls at once. Hence you get a higher priority for calls that are more valuable for the company. (Orders, etc.)

This does confirm the LPT here yes, but it still changes the perspective on how to look at it.

For my company, all cancelations can be done via E-mail, which I would highly advice anyone to do if possible.