Avoid inadvertent "Shut Down" of Mac

For a Mac mini or such acting as a server in a server room or colo, accidentally choosing the Apple > Shut Down… menu item is a major problem. Without physical access, you cannot start the Mac up again.

Is there a way to make it more difficult to inadvertently shut down a Mac?

One workaround is to set System Preferences > Energy Saver > Schedule (button) > Start up or wake (checkbox) to boot the computer, say 2:00 AM if you often do admin work at midnight. But I'm looking ways to avoid the shut down problem in the first place.