Service management is a closed-loop system. Why?

Various activities and unique tasks need to be performed throughout the ITIL Service Lifecycle, these tasks are nothing but processes and functions. These processes are organized sets of dependent activities that are created to achieve a specific objective, the sequence of the activities is determined by the dependencies between the activities. Processes are closed-loop feedback systems that uses feedback to self-reinforce and self-correct.

Also the PDCA cycle in Continual Service Improvement is also a "closed loop" feedback system, through this feedback system, the output or feedback from any stage in the Service Lifecycle can be used to identify improvement opportunities for any other stage. For example, outputs from the Problem Management process - which is part of the Service Operation stage -may point to the need for an improvement in the Service Design or Service Transition stages.

So , basically a service management plan needs processes which can only be a closed loop system to run and also to improve the services.

In fact, it is not only service management that is closed-loop system.  All kinds of management and life-cycle disciplines are indeed closed loop systems.

I am -academically speaking- a control systems engineer, closed-loop control systems is one of the core concepts in control theory.  I am also lucky to have worked in IT and later on in management consultancy services where the closed-loop control systems are also core concepts

The essence of the subject is that in all these things, closed-loop control is based on "feedback" representing the actual outcomes of the process, get "compared to preset/desired values", and "corrective management action" is taken accordingly  !I hope this answers the question !!