Very difficult to define "self-inflicted". What about a footballer who breaks a leg, a cyclist who falls off his bike or a kayaker who bangs his face on a rock etc? These are all activities we are being encouraged to do, so charging them would be wrong (I think) although their injuries are self-inflicted. Someone would have to make a big list of all the allowed and disallowed activities if they were going to charge. You could bet your life that someone would fall off a bike because they were drunk and a big court case would follow to decide whether or not they should pay for their treatment.
As another example, supposing I am walking along minding my own business, when a drunker reveller comes along,smashes my face in and knocks me unconscious. How do they know I'm not a drunker reveller without breathalysing me?