The distinction still matters without free will, because it's still a predictor of future behavior. A driver who crashes because of a preventable cause shouldn't be allowed to drive until the problem is resolved. If the problem is falling asleep, the solution may be simple (get more sleep?) or hard (narcolepsy), while anger issues are probably pretty difficult to provably solve.
Belief in free will has some seriously harmful effects on the way we deal with these situations. Most notably, it's the basis for a focus on punishment rather than rehabilitation. Deterrents don't work, largely because they don't fix the causes for bad behavior. Rehabilitation is the only sensible approach if you don't believe in free will, whereas punishment makes a bit more sense if you believe that people have free will.
> Perhaps someone can reframe that in terms of types of error, and people prone to more serious types of error (road rage) face different consequences. But that gets real complicated real quick.
This is fundamentally a free-will-based way of seeing the problem. "Consequences" are completely irrelevant in a deterministic worldview unless you can prove that they act as a deterrent (that is, that they are part of the cause). Since consequences are provably not significant deterrents for many crimes, I don't think that works.
Your argument basically that "this idea of punishment/consequences (which only makes sense in a free-will-based ideology) doesn't work in a deterministic ideology, and punishment/consequences are good in my free-will-based ideology, therefore deterministic ideologies are wrong". But you have to hold a free-will-based ideology for the preconditions of your argument to make sense.