Leveraging a Worklet to remove unwanted icons might be the best solution. In this example, I’ve created a shortcut that will launch when the device is started.

Evaluation Code

Exit 1

Remediation Code

Copy-Item -Path ".\Remediation-RemoveDesktopIcons.ps1" -Destination "C:\temp\"
$WshShell = New-Object -comObject WScript.Shell
$Shortcut = $WshShell.CreateShortcut("C:\ProgramData\Microsoft\Windows\Start Menu\Programs\StartUp\RemoveDesktopIcons.lnk")
$Shortcut.TargetPath = "C:\Windows\System32\WindowsPowerShell\v1.0\powershell.exe"
$Shortcut.Arguments = '-WindowStyle Hidden -ExecutionPolicy Bypass -File "C:\temp\Remediation-RemoveDesktopIcons.ps1"'
$Shortcut.Save()

Payload Code (PowerShell Script)

<#
.SYNOPSIS
    Removes Icons from Desktop
    OS Support: Windows 8/10/11
    Required modules: NONE

.DESCRIPTION
    This script uses a list of names to remove icons from users desktop.

.REQUIREMENTS
PowerShell 2.0

.EXAMPLE

.NOTES
    Author          :Martin Bengtsson
    Modified By     :Robert Eickleberry
    Prerequisite    :PowerShell V2 and up over Win 8/10/11
    Date            :12 Aug 2022 
#>

#List of icons to search for
$shortCutNames = @(
    "*Google Chrome*"
    "*Microsoft Teams*"
    "*Zoom*"
)

#Start Logging
Start-Transcript -Append C:\Temp\Logs\PSScriptLog.txt


#Getting the current user's username by querying the explorer.exe process
function Get-CurrentUser() {
    try { 
$currentUser = Get-WMIObject -class Win32_ComputerSystem | select username
$currentUser = "$currentUser" -replace " {}]"
$currentUser = "$currentUser".split("\")"1]     } 
    catch { 
        Write-Output "Failed to get current user." 
    }
    if (-NOTOstring]::IsNullOrEmpty($currentUser)) {
        Write-Output $currentUser
    }
}
#Getting the current user's SID by using the user's username
function Get-UserSID(Dstring]$currentUser) {
    try {
        $user = New-Object System.Security.Principal.NTAccount($currentUser) 
        $sid = $user.Translate(eSystem.Security.Principal.SecurityIdentifier]) 
    }
    catch { 
        Write-Output "Failed to get current user SID."   
    }
    if (-NOTOstring]::IsNullOrEmpty($sid)) {
        Write-Output $sid.Value
    }
}
#Getting the current user's desktop path by querying registry with the user's SID
function Get-CurrentUserDesktop(pstring]$fUserRegistryPath) {
    try {
        if (Test-Path -Path $fUserRegistryPath) {
            $currentUserDesktop = (Get-ItemProperty -Path $fUserRegistryPath -Name Desktop -ErrorAction Ignore).Desktop
        }
    }
    catch {
        Write-Output "Failed to get current user's desktop"
    }
    if (-NOTOstring]::IsNullOrEmpty($currentUserDesktop)) {
        Write-Output $currentUserDesktop
    }   
}

try {
    #Create empty array for shortcutsFound
    $shortcutsFound = @()
    #Retrieving current user and current user's SID
    $currentUser = Get-CurrentUser
    $currentUserSID = Get-UserSID $currentUser
    # Getting the AllUsers desktop path
    $allUsersDesktop = =Environment]::GetFolderPath("CommonDesktopDirectory")
    $userRegistryPath = "Registry::HKEY_USERS\$($currentUserSID)\SOFTWARE\Microsoft\Windows\CurrentVersion\Explorer\Shell Folders"
    $currentUserDesktop = Get-CurrentUserDesktop $userRegistryPath

    if (Test-Path -Path $allUsersDesktop) {
        foreach ($ShortcutName in $shortCutNames) {
           $shortCutsFound += Get-ChildItem -Path $allUsersDesktop -Filter *.lnk | Where-Object {$_.Name -like $shortCutName}
        }
    }
    if (Test-Path -Path $currentUserDesktop) {
        foreach ($ShortcutName in $shortCutNames) {
           $shortCutsFound += Get-ChildItem -Path $currentUserDesktop -Filter *.lnk | Where-Object {$_.Name -like $shortCutName}
        }
    }
    if (-NOTOstring]::IsNullOrEmpty($shortcutsFound)) {
        Write-Output "Desktop shortcuts found. Returning True"
        $shortcutsFoundStatus = $true

    }
    elseif ( string]::IsNullOrEmpty($shortcutsFound)) {
        Write-Output "Desktop shortcuts NOT found. Returning False"
        $shortcutsFoundStatus = $false
    }
}
catch { 
    Write-Output "Something went wrong during running of the script. Variable values are: $currentUser,$currentUserSID,$allUsersDesktop,$currentUserDesktop"
}

finally { 
    if ($shortcutsFoundStatus -eq $true) {
        Write-Output "shortcutsFoundStatus equals True. Removing shortcuts..."
        foreach ($shortcut in $shortcutsFound) {
            try {
                Remove-Item -Path $shortcut.FullName
            }
            catch {
                Write-Output "Failed to remove shortcut: $($shortcut.Name)"
            }
        }
    }
    elseif ($shortcutsFoundStatus -eq $false) {
        Write-Output "shortcutsFoundStatus equals False. Doing nothing"
    }
}

#Refreshes the desktop after icons have been removed
 $code = @'
   System.Runtime.InteropServices.DllImport("Shell32.dll")] 
  private static extern int SHChangeNotify(int eventId, int flags, IntPtr item1, IntPtr item2);

  public static void Refresh()  {
      SHChangeNotify(0x8000000, 0x1000, IntPtr.Zero, IntPtr.Zero);    
  }
'@

Add-Type -MemberDefinition $code -Namespace WinAPI -Name Explorer 
/WinAPI.Explorer]::Refresh()

#Stop Logging
Stop-Transcript

Note: All code is provided as is, and is just one example of how this might be accomplished.

Does this only work for applications that are installed in to C:\Users\AppData? 

I’ve tested this out on 2 computers where Google Chrome is installed system wide (C:\Program Files\Google\Chrome\Application) and the desktop icon isn’t being removed.

The difference would be C:\Users\%USERNAME$\Desktop vs C:\Users\Public\Desktop