You say you can ride 30 mph without "too much effort". I have a very hard time believing that. Eddy Merckx was the first cyclist to average 30 mph for an hour and that was a really big deal at the time. It was regarded as verging on the superhuman.
As for manuevering, bicycles manuever better than cars at those speeds. On mountain descents, cars can not keep up with skilled cyclists. As for braking, a bicycle is slower at braking than a car. The coefficient of friction is the same since both cars and bikes use tires made pretty much of the same stuff. However, bicycles tend to flip when they brake too hard and cars do not. Even that is not a major consideration. The major problem is the fact that motorists tend to pull out in front of cyclists, or turn in front of them. Motorists sometimes do not see the cyclists, other times they clearly see the cyclist and turn anyway. In this case, they either misjudge the speed of the cyclist or they figure that the cyclists will yield to them.