He's just not fit to have them unsupervised. He may be a binge drinker, but he couldn't limit his binging to when he didn't have them. Imagine being passed out when you have 2 young children in your care!
Why do you think the court won't award supervised visits only? You have an instance of him drinking and driving with the kids in the car, being passed out drunk while they were at his house, missing access dates because too drunk, and being obviously drunk in their presence. That sounds like a strong case to me.
You say he's a caring father. Maybe after the last episode even he can see they need better protection than he can provide. It would be different if he was able to limit his binges to when he's alone.