Sorry for being a little late to the conversation. I also agree that you generally have nothing to worry about although I have put a protector on my monitor.
I've done it for three reasons. First, I get into some pretty harsh desert environments when traveling, and while I usually use a ThinkTank Hydrophobia to protect everything from the blowing sands, I just want to be extra safe. Second, I am forever cleaning my skin oils and deposits off the LCD. While I use a lens cloth to do so, I rather clean off the cover I've put on the LCD, than the LCD myself. Last, is peace of mind. While it may be unnecessary, I'm more comfortable having the $32.95 protection on the LCD than not having in on.
I use a Giottos SP8306 AEGIS Professional Glass Optic Screen Protector - 12 Layer on the D4's monitor.