What is the theoretical ultimate purpose or point of 360 degree feedback?
The sole reason for using 360 degree feedback (its purpose, so to speak), is simple:
To provide information that the employee or receiver of the feedback can use to improve performance on the job.
That's the only purpose that makes sense. If the 360 system doesn't provide sufficient information, or quality, specific information that is good enough to allow the employee to improve, then it's a failure.
In practice, that's often the case.
However, some companies mistakenly believe that 360 degree feedback can be used to determine promotions, pay grades, bonuses and even to guide disciplinary action. That is problematic for a number of reasons, and amounts to management abdicating its primary responsibility for managing employees.