There is no such thing as Wounded (capital W meaning game rule status) in any version of D&D. There is Dead, Unconscious, or Conscious. Role-Playing wounded (small w referring to the general term) is the only way a wound exists in any edition. The status you attribute to being Wounded may not mesh with others. In fact, you mention that once Bruce Willis in Die Hard meets his objective he goes to the hospital to heal up. Once my players met their objective in Keep on the Shadowfell they rested to recover from their wounds. Could they have gone off to the next dungeon the next day? Yes, if the story called for it. But Die Hard 2 could have started with Bruce Willis being loaded into the ambulance. Someone runs up to tell him that his daughter was kidnapped by the real villain behind the scenes. If Die Hard were a 1E game, he would have to push on in a weakened state, probably putting his daughter in jeopardy when he can't fight the fight as long the next day or waiting to heal and losing his daughter for sure. In 4E he pushes himself up stiffly while the paramedics try to talk some sense into him. He pushes them away saying, "I've gotta save Sara!" You would still roleplay that he is hurt and struggling to continue, even at full hit points! Hit points have never equaled wounds to me. And wounds have never had a game effect in D&D. Other systems I've played that do have game effects for wounds have been fun, but PCs in them seem to suffer the death-spiral effect. Once you start getting hurt, it is harder to avoid getting hurt more.
It isn't badwrongfun to play a grittier game where hit points are hard to come by. Neither is 4E badwrongfun to emulate the action movies that many people love and adore, now matter how cheesy the dialogue gets at times.