(Non-US here)
As I understood it, this "immunity" is granted for POTUS doing things in the course of their responsibility as POTUS. Could it be argued that breaking laws & orders which bind the activity of POTUS is _inherently not_ the work someone in that role?
Isn't the point of immunity that it's immunity from prosecution on actions that are / would potentially be illegal? You don't need immunity if what you are doing is legal anyways.
Immunity is generally scoped. Challenging the determination of scope is not the same as challenging the action.
Immunity also isn't absolute. For example police in the US typically enjoy broad immunity but that doesn't imply not getting dragged into court. They just have sweeping legal defenses available to them that other people don't.