Correct me if I'm wrong, but I don't believe that quite fully restores the computer to a pristine state, because while it wipes the user data, it doesn't install a fresh copy of the OS. On a couple of occasions I've have issues with my Mac that have been solved purely by reinstaling the OS. Given that the OP is going to the trouble to start fresh, I'd advise them to reinstall the OS as well.
And while probably not of relevance to the OP, I'll note this as a point of interest: Generally speaking, MDM (mobile device management) software, which businesses install on company-owned machines, cannot be removed by the user, even if they completely wipe the disk and reinstall the OS. I don't know how it works; perhaps it's installed on a hidden partition to which the user doesn't have access. It can only be removed by the company that installed it (or the company that makes the software).