I help manage all the iPhones for our company. I can assure you that we would NEVER hand out an expensive device like this without having 1. a case or 2. a screen protector.
We use the Zagg Invisible Shield and there is nothing "annoying" about it. You can't even tell it's on the device. It comes with a lifetime guarantee as long as you register it. If anything happens to it - if it cracks, peels off, shatters, etc. - you make a warranty claim, they send you a new one for the price of shipping along with a return envelope for the new one. I can't even tell you the numbers of screens it has saved for us.
I hear people saying, "Oh, I don't want to put anything on the phone and mess with the beauty of it." Well, how beautiful is it when you inevitably drop it and the screen is all scratched up or shattered? We just don't take that chance here, because we do resell the devices after they're upgraded, and want to get top dollar for them.