Proven? To whom?

Never heard about people killed in crash caused by drunken driver ? Or pedestrians hit by cars driven by drunked drivers ?

Excessive alcoholism is known to cause harm. Should we make being an alcoholic illegal? Wouldn’t that make it harder for alcoholicsnto try to get help, for fear of being arrested instead of getting help, much like what happens to drug addicts?

No, we should just have laws try to avoid consequences for others Are you an alcoholic ? Ok, we will help you to be ok but at the same time we try to avoid you drive while drunk. It not seems too unreasonable

People get hurt constantly while fishing, too. Should we make fishing illegal?

Point is: how probable is that someone fishing hurts someone else ? How much damage you can do ?
Again, the point is not to make something illegal because you can hurt yourself, it is about trying to have law that try to prevent you hurt someone else while doing something.
If fishing can hurt others, maybe we should have a law that, while not forbidding to fish, protect the others from what you are doing. I would imagine that you would not like to swim in the sea while someone is fishing with bombs (illegal) 2 meters away from you, don't you ?

The problem is where do we draw the line. You want to draw it at some possibility of harm to others. I want to draw it at actual harm to others.

Fine as long as you accept the consequences. I just don't agree with you.

Which of these is more or less likely to wind up being stretched over time?

Both, because you just need to redefine what "harm" means. And some people is good to do it.