You’re right that the drunk driver is only responsible for the first drink. The first drink is what caused the accident in the first place. What happened to manslaughter isn’t murder anyways? That drunk driver very much chose to drink that night and didn’t take measure to stop themselves from doing something dangerous, which justifies a manslaughter charge, like getting a ride to the bar.
That’s very different from someone being mentally ill and absolutely unable to control when those voices start screaming in their head to kill someone.