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The command that effectively sets the Finder to show mounted servers on the desktop involves using the 'defaults write' syntax. This command updates or creates a preference value in the specified domain, which in this case is com.apple.finder. By adding the ShowMountedServersOnDesktop key and setting its value to true, you instruct the Finder to display any mounted servers directly on the desktop.

This command is particularly useful for users who want quick access to their networked servers or remotely mounted drives, enhancing productivity by ensuring that these resources are easily visible and accessible right from the desktop.

The other options do not achieve this purpose. For instance, using 'defaults cat' or 'defaults read' would only display existing values and not modify them. The 'defaults append' command is also incorrect in this context, as it does not apply to altering the state of showing mounted servers directly on the Finder’s desktop. Thus, 'defaults write com.apple.finder ShowMountedServersOnDesktop true' is the correct approach to achieve the desired setting.