I do think it is important to make a distinqtion, on slow traffic lanes we do not have separated traffic lanes(20 mph), but on faster lanes (30 mph and above) we do have separated lanes. We also have bike lanes without any car lanes in the coutryside, just for commuting between towns. Kind of like a bike highway.

Some people are right intersections are problems, but on busy intersections we have either bike traffic lights, a roundabout with clear signs on which has priority(mostly cyclists) or an underpass/overpass for cyclists.
It is clear to everybody that the intersections are the most dangerous place, thus everybody is checking if everybody is following the rules. This makes it more safe. Accidents do happen, but very rarely and almost always with cars or bikes running red lights. It is always wise to check that everybody is following the rules before crossing and to follow the rules yourself. But in the Netherlands cycling is as safe as walking down the street. I my opinion cycling in NY, DC or LA would be great if only their were good facilities. If it is fast people will use it, because cycling has a lot of benefits, like it is cheap and can be faster than a car in a city.

Curitiba is one of the most modern capitals in Brazil. Here we got pioneers in articulated buses and other concepts.