I agree with your entire post, almost. I think there really are people out there that don't deserve kids. Not because they are druggies or alcoholics or anything, just because they are horrible people, Joseph Fritzl springs to mind.
Also, I know an alcoholic who is a dad, it is not ideal and he is far from perfect. But jeez he loves his kids and he would lay his life down for them. It is so sad to see him slowly killing himself. But as you said, a lot has to do with Mental illness, and it doesn't make him bad or evil, just unwell