I've used Nikon SLR and DSLRs for over 40 years. I've never had any hot shoe protector, I've never had any hot shoe problems either. I wouldn't worry about it.
Gary in SE Michigan, USA. Nikonians membership - My most important photographic investment, after the camera. D4, D810, D300 (720nm IR conversion), D90, F6, FM3a (black), FM2n (chrome) YashicaMat 124, Graflex Speed Graphic 4x5 My Nikonians Gallery & Our Chapter Gallery
I got my F80 brand new from B&H, and it had one. I kept it on the camera until it fell, got lost, probably missed it days after I lost it. The camera survived well without it. Hence, don't worry about it; it's just packaging to me.
It's just in the way when you want to use the flash. The only purpose it may have: If you want to take you camera into the rain forest then maybe it will provide some protection for the flash contacts. In that case, B+H sells it for $3, or you can take a wild gamble and buy it for $2 used at B+H
Nikon probably uses it to ensure that the camera is environmentally sealed. I don't think it will fall out accidentally because in mine it's pretty stuck in there. I have a small pouch in my Lowepro neck strap for memory cards but I use it to small things like this cover and the older D200 GPS and trigger connector screw-in caps (those were the worst to loose!).
It happened so long ago that I do not remember the details, but, I received a painful shock when my nose came in contact with the uncovered hot shoe. I do not remember if I was shooting with a Nikon; I do not remember if I was PC connected to a studio flash unit; I do not remember if my nose was wet; but I do remember the pain. As a result, if I have that little piece of plastic for the hot shoe, I use it.
Also keep in mind that some cameras (I don’t think that includes Nikons) are designed to shut off the built-in flash if anything like a flash unit or a piece of plastic is detected in the hot shoe. I learned this the hard way when I loaned a Canon to a friend and stuck a little plastic thing in the hot shoe to protect it from damage. When she returned from her vacation, she complained that she could never get the built-in flash to work.