I have the same problem, but in my case there is a warning message. When I try to create a Desktop shortcut for SKSE from inside Mod Organizer (click on Shortcut, select Desktop from drop-down list), the following message is given in an Error window:
failed to create C:/Users/<my username>/Desktop/SKSE.lnk
Where <my username> is a placeholder for my Windows account name. My operating system is Windows 10 64-bit Home. The Desktop folder has full permissions for the current user (me). The account has administrator privileges. if this post is considered late, I am sorry beforehand for necromancing a thread. I didn't want to create a new thread since this is already on-topic.