Is it necessary to describe processes precisely? Most people say no. It is good enough to describe the most important execution variants of a business process. Eighty percent coverage is good enough. The rest is handled by humans according to the concrete situation.
By the way: precise specifications are different from detailed specifications. Precise specifications define the allowed sequences of actions to be executed by the parties involved in a process. And for that description a language has to be used which has a precise semantic. All the involved parties need to understand process descriptions in the same way. In general involved parties can be people and/or IT-Systems. This means a language must be understandable by both types of actors.
If in a process alternatives are allowed for human decisions then it must be defined when this is possible and what the alternatives are.
Precise process specifications define the cooperation of the involved parties. They do not describe the details of an action executed by a certain actor. These details are part of the implementation. Only the impacts of action results on the cooperation behavior must be described.
Do you think that precise process specifications are a waste of time and money? What would happen if Amazon had not described its processes precisely? What would it mean for Amazon if they had not precisely defined how an order change request of a customer needs to be handled? What would that mean for you as a customer?