As a regular cyclist, I would say that requiring a license from cyclists would certainly do something to fix this: make cyclists more aware of it.
Over here, about 2/3 of collisions between motor vehicle and bicycle are fault of the motor vehicle driver. But that leaves 1/3 where cyclist errors or breaches of traffic code are reason, which is also significant.
And then there are actually quite many cyclist accidents that do not involve a motor vehicle.
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.
Here, a motor vehicle was involved in 62 % of all bicyclist deaths over the period 2011-2015 (116 cases). Motor vehicle was not the guilty party in all of those (but in roughly 2/3 of them). So, motor vehicle driver was at fault in about 40 % of cyclist deaths.
Without any breakdown of who was at fault in the other accidents your stats still indicate that in comparison between bikes and motor vehicles, motor vehicle drivers are still twice as likely to be at fault. Retrain them before you retrain cyclists.
I don't necessarily say that requiring a license from cyclists is what I want. However, I do think that some training and education of cyclists would certainly help. I also see some cyclists who have clear attitude problems. So retraining - or perhaps re-orienting - everyone would help.
Why can't we retrain both? Do we have to pick one or the other?
So make better use of the time and money: create safe infrastructure or - as a better investment train those that already have a license requirement and that insist on moving around tons of steel. Maybe increase the number of hours in school that deal with safe conduct in traffic. Or - gasp - fine the people blocking cycle lanes and otherwise endangering cyclist hard.
Improve cycling by all means, but use something that is effective: better infrastructure, education, enforcement. The Berlin police introduced a police squad on cycles a few years ago in one district and that has proven to be a very effective method: For one, they enforce road rules for people on bicyclist, but the major effect is that they remove cars from infrastructure dedicated to bicycles which in turn actually enables cyclists to use that infrastructure and makes people less likely to ride on the sidewalk, for example.
Calling for education of cyclists has a strong smell of victim blaming. Oh, sorry, he's dead. If he'd been better educated, he might have known that he was in the right.
Statistics show that in the large majority of cases of accidents between cycles and motor vehicles, the driver of the motor vehicle is at fault. Requiring a license for cycles will do just about nothing to fix this. Just yesterday I was nearly run over by a car turning left into the oncoming cycle lane and by another one who thought that the pedestrians traffic light applies to bicycles. My knowledge that I was correct in both cases did not help the least bit.
So maybe yearly retraining for drivers of motor vehicles would be a better move.