To always show the Computer icon on the desktop via GPO, there are several things to be set. Aside of the obvious setting in GPO, you also have to add a registry entry through GPP to automatically show the Computer icon on desktop.

In User Configuration, Preferences, Windows Settings, Registry, add a new entry. Whether you want to enforce or not, is up to you. Either choose create (only applied once), or Replace (always apply).

The value is a DWORD value in HKEY_CURRENT_USER\Software\Microsoft\Windows\CurrentVersion\Explorer\HideDesktopIcons\NewStartPanel, named {20D04FE0-3AEA-1069-A2D8-08002B30309D}. This is the CLSID for the Computer icon. Set it to 0 to have the icon shown on user's desktop.

There are other CLSIDs present for other icons on the desktop (Network, User's folder, etc.). They can be added in the same way.