Many years ago, the world was a very different place. Wives greeted their husbands at the door with perfect smiles on their faces and all children were well-behaved. This was a time when all concerns were petty, the villains just misunderstood goofs and doctors knew how to show a hard-working superhero some damn respect.
Privacy may be a foreign concept to us today, but back all those many years ago, a surgeon in a superhero comic would look at the badly injured masked man in front of him (and Daredevil has been badly injured more times than most) and just say to himself and his surgical crew: “You know, let’s just leave that mask on. He is probably wearing it for a reason.” And, because these were more innocent times when the idea of wearing a mask to cover up illegal activities was far from the average person’s mind, the mask would stay on. Below are panels from Daredevil #96, by Gerry Conway and Gene Colan: