You are assuming that this 1/3rd is due to lack of knowledge - I question that assertion. And still, regular retraining of motor vehicle drivers would still be a better investment. They choose to move a ton of steel around in a manner that's potentially dangerous to others and they cause twice as many accidents, despite having a license requirement.
> And then there are actually quite many cyclist accidents that do not involve a motor vehicle.
Those tend to be less severe. Last years stats for Berlin: All cyclists killed were killed in an accident with a motor vehicle. Most common causes: dooring, right turn accidents, mostly trucks, one cyclist running a red light.