You have a really good point.
Cyclists were on the road before cars were, and have become 'secondary' because cars are faster. Mixing cyclists with cars is a very dangerous idea.
A lot of pedestrians (wrongly) see cyclists as a nuisance on the pavement, and want them to stick to the road. Many cyclists are killed in road accidents, but very few pedestrians are ever injured by a cyclist.
Part of the problem is that many cyclists are proud of how fast they can go, and consider themselves 'traffic'. If speed was the point of cycling, then the bicycle would have become obsolete. Cycles are better because they cause less congestion, are more manoeuvrable, and can mix safely with pedestrians. Of course, the cyclist needs to be considerate to pedestrians and other cyclists to do so; many aren't. A proper speed for cycling does not make you sweat; you should be able to commute in your working clothes.
Unfortunately, facilities are not routinely provided for proper cycling. Many people need to commute so far that cycling isn't practical, or would need to be done fast. This is because workplaces are usually 'zoned' together in one part of a city, and homes are clustered somewhere else.
'Cycle lanes' are randomly painted onto roads to qualify for funding targets, so they don't connect places where cyclists want to be. They are inconvenient and often dangerous to use. Cycle parking is usually an afterthought, and of poor quality. Usually, it's less weatherproof, and less secure, than the car-parking nearby.
Cyclists have to put up with all of this, as well as the danger from inconsiderate drivers of cars and lorries. They often develop an aggressive style of riding, to help them cope with the difficulties.
On behalf of cyclists, I'm sorry you had to experience the problem so suddenly. Thank you for handling it well, and avoiding any injuries.
You should also bear in mind that you can be put in just as much danger, by something falling off a car just in front of you. By remaining aware of the possible hazards all the time while you are driving, you can maximise your chances of coping well each time something unexpectedly goes wrong.