What exactly falls under the "other security-related tasks" section? The only thing I can think of would be for a privileged application to try and hide things from the OS.
Apart from being able to hide from the OS a hypervisor is also safe from manipulation by the OS and can observe and manipulate anything the OS does.
This opens a few doors: debugging or reverse engineering the OS or kernel modules, sandboxing a system you don't trust, detecting rootkits, protecting your antivirus solution from malware, etc.
