I've had no end of troubles with disappearing desktop icons with CrossOver installed. As soon as I removed it, all the problems went away. I'm not certain, but I think it's the "CD detector" component that does it.
Go into System Preferences, click on Accounts, choose your account on the left, and then click Login Items on the right. Remove the list item CROSS OVER CD HELPER (or similar) by single clicking it and then clicking the - just below the list. This will stop that program from running when you start up your computer . If you now restart, it should all be back to normal.
If that doesn't work, try just changing the displayed items on your desktop to 'refresh' the settings.
Click on the desktop, go View at the top, and just try fiddling around with the icon size. If nothing appears then, then close that little window and press Command + , (comma). This will bring up the preferences window for Finder. Click General at the top, and then try un-ticking some of the boxes, and re-ticking them.
Okay, well AppZaper is quite comprehensive, but follow this guide on the CrossOver site to ensure everything has been removed. I don't think a reinstall is necessary at this stage. Hopefully it won't come to that.