The Netherlands was as car-supremacist a country as any other until the 70s. They fixed their stuff and now their bike infrastructure is excellent: people move to their destinations faster and safer and cheaper and cleaner than in everyone had to travel in an automobile.
Bikes cannot be faster than cars because cars can literally accelerate faster and have higher top speed. When car infrastructure is sufficient there is no theoretical way bikes can move people faster as you claim. As for safer - cars are very safe already and it is irrational to care about minor risks.
Cars are big, and during rush hour have an average of roughly one person in them. Cities are confined spaces with lots of people living in them. As such, you are condemned to have traffic jams when cars are the main form of transport.
To make car infrastructure "sufficient" you are required to make roads wider, which reduces the quality of life of those living in the city, and perversely increases the demand for car transport eventually leading to more traffic jams. Bikes, even in high traffic situations, move faster than cars that are stationary.
And yes, cars are very safe — but only for those inside of them. As they get bigger, heavier and with taller bumpers they get more and more deadly for pedestrians and cyclists.
It hasn't always been like that. There was a public campaign in the 1970s to try to prevent all the child deaths from car drivers - Stop de Kindermoord. There's not really any excuse for continuing to design purely for car drivers apart from that's what people have been led to believe.
People often say "this is why we can't have nice things"... Such policies are the "nice things".