Out-File seems to force the BOM when using UTF-8:
Out-File
$MyFile = Get-Content $MyPath $MyFile | Out-File -Encoding \"UTF8\" $MyPath
This one works for me (use "Default" instead of "UTF8"):
$MyFile = Get-Content $MyPath $MyFile | Out-File -Encoding "Default" $MyPath
The result is ASCII without BOM.