Putting the joke aside, I've always seen hps as toughness. When you lose hps, your toughness is being taxed and depleted. YOu're not getting an actual injury - just scuffs and bruises. Fire breathes dragon and deals 48 fire damage to you? Well, you turned your body away and protected your vulnerable parts. It took a bit out of you, but you didn't actually get third degree burns across your entire body.
So why does cure wounds work on you, then? Well, I treat it as curing those scuffs and bruises while it refreshes you. It doesn't fix your real wounds, right? If someone blinds you by sticking a stixk in your eye, cure light wounds taking you to fll does not restore your vision, right? Other spells restore your lost functionality.