Ice Cream Sand Witch

So that you can't see their eyes staring at people's booties.

The eyes are windows to the soul. They display emotion and tells all too easily... and generally speaking, when you're guarding someone of high import, you'd want to look like you always have some command of the situation, even when you're secretly shitting yourself in panic.

It's like asking why a cop would were them, same basic concept...

aviators are especially popular because they hide the eyebrows. It's a method of psychological stealth