This could not apply to Copenhagen and Denmark but I guess that in most other countries cyclists are also car drivers and spend more time in their car than on their bicycle. However there are many car drivers that don't have a bicycle or seldom use it, maybe because they are scared by cars. If the driver is not a cyclist it's difficult to understand what's going on. I suggest that to get a license one should also get some practice in the traffic as a cyclist, to remember what not to do with a car.

About your mitigation strategy: that would solve the problem but unfortunately the cyclist won't stop behind the car. The cyclist would turn left to overtake the stopped car. I don't like to do that because it puts me in the middle of the road or to the right of another car. It also requires some space to maneuver and a car could be arriving from behind me and close the gap.

Usually stopped cars don't hit cyclists (but watch out for doors). I look at the traffic light and refrain from overtaking the car (both on the left and on the right) if it's about to turn green.