As Per Larsen blogged this week, the recent Edge stable release now has a new MSI parameter to skip the desktop shortcut.  From the release notes:

Added an MSI command line parameter that lets you suppress Desktop icon creation when you install Microsoft Edge. The following example shows how to use this new parameter:
MicrosoftEdgeEnterpriseX64.msi DONOTCREATEDESKTOPSHORTCUT=true
There will be a group policy to support this functionality in an upcoming release.

That’s much easier than the transform method that I blogged about previously, and directly resulted from the Twitter discussion with the Edge team around this.  And, it will get even easier in the future with a new GPO setting for configuring the same thing.

I do wish this would be the default when deploying Edge via Intune (where Intune takes care of downloading the latest Edge bits for you), but right now there are no options exposed to do this on the Edge app type, and it’s not the default behavior either.  Maybe at some point in the future.  Until then (or until the GPO arrives), you can download the Edge MSI (three times if you want to support x86, x64, and ARM64), upload it to Intune as a new Win32 app (three times, packaging it into a .intunewin file), and include the DONOTCREATEDESKTOPSHORTCUT=true parameter on the command line.