Why does a mistake about a fact belonging to the type destroy the intentional offence, while a mistake about the prohibition leaves the offence standing with a reduced penalty?

C. Type intent is negated by factual mistake, but prohibition mistakes merely lessen reproach

Because the two mistakes attack different stages. A mistake of type means the person did not know a fact that makes the conduct fit the offence, so intent, which sits in the type, is gone and only negligence remains. A mistake of prohibition leaves intent untouched and diminishes the reproach at the culpability stage instead.