Wolverine is a very flawed but human character, but that's the whole point. He's not Superman. He's not even Batman. Wolverine is a damaged person who grew into the best person he could possibly be despite his anger, resentment, anxiety, loss, and pain. That's what makes him such an interesting character.
His Healing Factor may be physical, but it's also symbolic of his emotional healing factor. That no matter how much pain, death, or misery comes his way he keeps going...although not without his scars.