Cortana is not running as part of Windows Server 2016 by default . The default install option is no GUI and that option does not install Cortana. You will explicit have to choose that you want to install the "Desktop experience" in order to get Cortana. If you select to add an optional feature named "Desktop experience" it is fair enough that Cortana is there since she is (or now was) a part of Microsoft Desktop experience. Most typical server workloads run fine without the GUI (and Cortana).
Windows Server 2016 Installation Options: https://docs.microsoft.com/en-us/previous-versions/windows/d...