Let's take a look at full contact, as well as boxing. In training a competitor/boxer wears protection such as hand tape, gloves and a mouth piece. What is the reason? To protect the hands from injury and/or being cut. Herein lies the issue, you (generic you) won't have these items in a real world attack. The chance of injuring the hands, particularly when striking the face/head is substantial. Anyone that has broken a knuckle, sprained a wrist, cracked a metacarpal etc knows that in addition to being painful, it can interfere with otherwise simple tasks i.e. using a cell phone to call for help, utilize car keys to initiate an escape (or to unlock a door), manipulate an improvised or concealed weapon etc. Damage to the hands may reduce the use of the hand to effect escape, further defend against attack or assist another. Furthermore, if the hand is cut, for example by punching someone in the mouth or other area of the head (which bleeds pretty readily) we now have to be concerned with blood-born pathogens. This is a real concern, particularly these days with the use of intravenous drugs, poor living conditions etc. I cannot emphasis this enough! Therefore boxing or continuous strikes to the head with unprotected hands is not the best of possible options.
So there is a possibility of hurting your hands if you hit someone in the head with them. Shouldn't you be saying this to all the people who think that face punching can neutralize a taekwondo competitor whose arms are dangling down by their sides as they bounce up and down like a jack hammer? Doesn't that apply to them more so than to a taekwondo competitor who some argue cannot punch?